a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

yang lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 d 7 we have extended in most cases through 24th order the series expansions of the dimer density in powers of the activity in the case of bipartite hyper simple cubic and hyper body centered cubic lattices of dimensionalities 2 d 7 a numerical analysis of these data yields estimates of the exponents characterizing the yang lee edge singularities for lattice ferromagnetic spin models as d varies between the lower and the upper critical dimensionalities our results are consistent with but more extensive and sometimes more accurate than those obtained from the existing dimer series or from the estimates of related exponents for lattice animals branched polymers and fluids we mention also that it is possible to obtain estimates of the dimer constants from our series for the various lattices

critical behavior of the q 3 4 potts model on quasiperiodic decagonal lattices abstract in this study we performed monte carlo simulations of the q 3 4 potts model on quasiperiodic decagonal lattices qdl to assess the critical behavior of these systems using the single histogram technique in conjunction with the finite size scaling analysis we estimate the infinite lattice critical temperatures and the leading critical exponents for q 3 and q 4 states our estimates for the critical exponents on qdl are in good agreement with the exact values on 2d periodic lattices supporting the claim that both the q 3 and q 4 potts model on quasiperiodic lattices belong to the same universality class as those on 2d periodic lattices

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

amplitude ratios and β estimates from general dimension percolation moments low concentration series are generated for moments of the percolation cluster size distribution gamma j sj 1 s is the number of sites on a cluster for j 2 8 and general dimensionality d these diverge at pc as gamma j approximately aj pc p gamma j with gamma j gamma j gamma j 2 delta where delta gamma beta is the gap exponent the series yield new accurate values for delta and beta delta 2 23 or 0 05 2 10 or 0 04 2 03 or 0 05 and beta 0 44 or 0 15 0 66 or 0 09 0 83 or 0 08 at d 3 4 5 in addition ratios of the form ajak aman with j k m n are shown to be universal new values for some of these ratios are evaluated from the series from the epsilon expansion epsilon 6 d and exactly in d 1 and on the bethe lattice the results are in excellent agreement with each other for all dimensions results for different lattices at d 2 3 agree very well these amplitude ratios are much better behaved than other ratios considered in the past and should thus be more useful in characterising percolating systems

series study of random percolation in three dimensions new high density series data for the mean number percolation probability and susceptibility of finite clusters are presented for bond and site percolation on four standard three dimensional lattices a pade approximant analysis of both high and low density series makes particular use of the rather precise unbiased estimates of the percolation threshold pc obtained recently by heermann and stauffer 1981 for the simple cubic lattice for this lattice the authors obtain the biased estimate gamma 1 73 or 0 03 for the site problem and a similar estimate but with larger uncertainties for the bond problem such a value is significantly larger than earlier series estimates assuming gamma to be universal they obtain precise although biased estimates of pc for both bond and site percolation on all four lattices using the bond estimates of pc they find an overall biased estimate of beta 0 454 or 0 008 for bond percolation on all three dimensional lattices the corresponding site problem requires further study scaling estimates of other critical exponents are alpha 0 64 or 0 05 delta 4 81 or 0 14 delta 2 18 or 0 04 nu 0 88 or 0 02 and nu 0 03 or 0 03

phase diagrams and cluster expansions for low temperature models i the phase diagram low temperature phase diagrams of two dimensional open image in new window quantum field models are constructed let open image in new window lie in an r 1 dimensional space of perturbations of a polynomial withr degenerate minima perform a scaling open image in new window and assume 1 we constructk distinct states on left begin array 20 c r k end array right hypersurfaces of codimensionk 1 in the space of perturbations an expansion is used to exhibit exponential clustering of the schwinger functions of each of these states at the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima we draw on ideas of pirogov and sinai 24 for this problem

rigorous lower bound on the dynamic critical exponents of the swendsen wang algorithm we prove the rigorous lower bound z sw v for the dynamic critical exponent of the swendsen wang algorithm for two dimensional q state potts models with q 2 3 4 this implies z sw 0 2 5 1 we present numerical data indicating that z sw 0 55 0 03 0 89 0 05 for q 3 4 95 confidence limits statistical errors only the discrepancy for q 4 appears to be caused by multiplicative logarithmic corrections

theory of minimum spanning trees ii exact graphical methods and perturbation expansion at the percolation threshold continuing the program begun by the authors in a previous paper we develop an exact low density expansion for the random minimum spanning tree mst on a finite graph and use it to develop a continuum perturbation expansion for the mst on critical percolation clusters in space dimension d the perturbation expansion is proved to be renormalizable in d 6 dimensions we consider the fractal dimension d sub p of paths on the latter mst our previous results lead us to predict that d sub p 2 for d d sub c 6 using a renormalization group approach we confirm the result for d 6 and calculate d sub p to first order in epsilon 6 d for d 6 using the connection with critical percolation with the result d sub p 2 epsilon 7 o epsilon sup 2

finite time scaling via linear driving application to the two dimensional potts model we apply finite time scaling to the q state potts model with q 3 and 4 on two dimensional lattices to determine its critical properties this consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields from the finite time scaling of the order parameter the coercivity and the hysteresis area and its derivative we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature the static critical exponents obtained in general and the magnetic exponent ensuremath delta in particular agree reasonably with the conjectured ones the dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short time dynamic results for q 4 our results also suggest an alternative way to characterize the weak universality

spectral properties of a periodically kicked quantum hamiltonian we study the spectral properties of the floquet operator for the periodically kicked hamiltonianh t h 0 t nt h 0 being self adjoint and pure point we show that the floquet operator is pure point for almost every if is cyclic forh 0 and has absolutely convergent expansion in the basis of eigenstates ofh 0 when this last condition is not satisfied the floquet operator can have a continuous spectrum as we show by an example

classical lattice gas model with a unique nondegenerate but unstable periodic ground state configuration we construct a classical lattice gas model with a unique periodic ground state configuration such that the peierls condition is not satisfied the ground state configuration is nondegenerate which means that for any fixed energye and any integern the diameter of the support of alln connected local excitations with energy less thane is bounded nevertheless the configuration is not stable it does not give rise to a low temperature phase any translation invariant gibbs state of our model corresponds to quasiperiodic ground state configurations this requires the modification of a recent hypothesis of dobrushin and shlosman

exact finite size scaling corrections to the critical two dimensional ising model on a torus we analyse the finite size corrections to the energy and specific heat of the critical two dimensional spin ising model on a torus we extend the analysis of ferdinand and fisher to compute the correction of order l 3 to the energy and the corrections of order l 2 and l 3 to the specific heat we also obtain general results on the form of the finite size corrections to these quantities only integer powers of l 1 occur unmodified by logarithms except of course for the leading log l term in the specific heat and the energy expansion contains only odd powers of l 1 in the specific heat expansion any power of l 1 can appear but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion

stochastic simulation of nonstationary oscillation hydroclimatic processes using empirical mode decomposition 1 nonstationary oscillation nso processes are observed in a number of hydroclimatic data series stochastic simulation models are useful to study the impacts of the climatic variations induced by nso processes into hydroclimatic regimes reproducing nso processes in a stochastic time series model is however a difficult task because of the complexity of the nonstationary behaviors in the current study a novel stochastic simulation technique that reproduces the nso processes embedded in hydroclimatic data series is presented the proposed model reproduces nso processes by utilizing empirical mode decomposition emd and nonparametric simulation techniques i e k nearest neighbor resampling and block bootstrapping the model was first tested with synthetic data sets from trigonometric functions and the rossler system the north atlantic oscillation nao index was then examined as a real case study this nao index was then employed as an exogenous variable for the stochastic simulation of streamflows at the romaine river in the province of quebec canada the results of the application to the synthetic data sets and the real world case studies indicate that the proposed model preserves well the nso processes along with the key statistical characteristics of the observations it was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model especially for hydroclimatic data sets that embed nso processes

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

diffusion percolation i infinite time limit and bootstrap percolation several models for the dynamic growth of percolation clusters or diffusion percolation dp are introduced and analysed in these models a random walker an ant walks on percolation clusters which are occupied with initial site concentration pi the ant is allowed to step off such clusters and add new sites to them if certain conditions are met some of these models are shown to have a one to one correspondence with models of bootstrap percolation bp in which sites which do not have a required number of neighbours are successively culled two new percolation thresholds have been calculated for two diffusion percolation models on the square lattice

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

sensitive dependence and entropy for quantum systems an attempt is made to carry to quantum mechanics the notion of sensitive dependence to initial conditions a few simple examples and properties are described for the entropy of quantum evolution a quantity is proposed in the spirit of the brin katok definition which characterizes orbit complexity rather than the state reduction nature of the quantum measurement process

kronecker s double series and exact asymptotic expansions for free models of statistical mechanics on torus for the free models of statistical mechanics on torus including the ising model dimer model and gaussian model exact asymptotic expansions of free energy internal energy and specific heat in the vicinity of the critical point are found it is shown that there is a direct relation between the terms of the expansion and kronecker s double series the latter can be expressed in terms of the elliptic functions in all orders of the asymptotic expansion

logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

cluster method for the ashkin teller model a cluster monte carlo algorithm for the ashkin teller at model is constructed according to the guidelines of a general scheme for such algorithms its dynamical behaviour is tested for the square lattice at model we perform simulations on the line of critical points along which the exponents vary continuously and find that critical slowing down is significantly reduced we find continuous variation of the dynamical exponent z along the line following the variation of the ratio alpha nu in a manner which satisfies the li sokal bound z cluster geq alpha nu that was so far proved only for potts models

renormalized field theory of collapsing directed randomly branched polymers we present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition we develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition for the swollen phase we find that by choosing model parameters appropriately our stochastic functional reduces to the one describing the relaxation dynamics near the yang lee singularity edge this corroborates that the scaling behavior of swollen branched polymers is governed by the yang lee universality class as has been known for a long time the main focus of our paper lies on the collapse transition of directed branched polymers we show to arbitrary order in renormalized perturbation theory with ensuremath epsilon expansion that this transition belongs to the same universality class as directed percolation

finite size scaling for potts models recently borgs and koteck developed a rigorous theory of finite size effects near first order phase transitions here we apply this theory to the ferromagneticq state potts model which forq large andd 2 undergoes a first order phase transition as the inverse temperature is varied we prove a formula for the internal energy in a periodic cube of side lengthl which describes the rounding of the infinite volume jump e in terms of a hyperbolic tangent and show that the position of the maximum of the specific heat is shifted by m l inq e l d o l 2d with respect to the infinite volume transition point t we also propose an alternative definition of the finite volume transition temperature t l which might be useful for numerical calculations because it differs only by exponentially small corrections from t

on model selection criteria in multimodel analysis 1 hydrologic systems are open and complex rendering them prone to multiple conceptualizations and mathematical descriptions there has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to 1 rank these models 2 eliminate some of them and or 3 weigh and average predictions and statistics generated by multiple models this has led to some debate among hydrogeologists about the merits and demerits of common model selection also known as model discrimination or information criteria such as aic aicc bic and kic and some lack of clarity about the proper interpretation and mathematical representation of each criterion we examine the model selection literature to find that 1 all published rigorous derivations of aic and aicc require that the true model having generated the observational data be in the set of candidate models 2 though bic and kic were originally derived by assuming that such a model is in the set bic has been rederived by cavanaugh and neath 1999 without the need for such an assumption and 3 kic reduces to bic as the number of observations becomes large relative to the number of adjustable model parameters implying that it likewise does not require the existence of a true model in the set of alternatives we explain why kic is the only criterion accounting validly for the likelihood of prior parameter estimates elucidate the unique role that the fisher information matrix plays in kic and demonstrate through an example that it imbues kic with desirable model selection properties not shared by aic aicc or bic our example appears to provide the first comprehensive test of how aic aicc bic and kic weigh and rank alternative models in light of the models predictive performance under cross validation with real hydrologic data

high order behaviour of the critical exponents for the scalar phi3 model with imaginary coupling for real coupling constants the vertex functions for the phi 3 model have a real and imaginary part the author presents a method of renormalising both parts of the vertex functions for small coupling g0 a consequence of the method is that the renormalisation group functions develop a non perturbative imaginary part this leads to an imaginary part for the critical exponents valid for 6 d epsilon 0 where d is the dimension of the space a dispersion relation in epsilon then yields the high order behaviour of the critical exponents as a power series in epsilon in particular the values of the overall universal coefficients c of the factorial growth are obtained

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

a nonparametric wet dry spell model for resampling daily precipitation a nonparametric wet dry spell model is developed for resampling daily precipitation at a site the model considers alternating sequences of wet and dry days in a given season of the year all marginal joint and conditional probability densities of interest e g dry spell length wet spell length precipitation amount and wet spell length given prior to dry spell length are estimated nonparametrically using at site data and kernel probability density estimators procedures for the disaggregation of wet spell precipitation into daily precipitation and for the generation of synthetic sequences are proffered an application of the model for generating synthetic precipitation traces at a site in utah is presented

susceptibility amplitudes for the three and four state potts models abstract the finite lattice method of series expansions is used to calculate a number of extended series for susceptibilities of the three and four state potts models on the square lattice we analyse all these series and estimate their critical amplitudes we resolve an uncertainty in amplitude ratios for high to low temperature susceptibilities and thus provide confirmation of field theoretic predictions

high temperature series analysis of the free energy and susceptibility of the 2d random bond ising model abstract we derive high temperature series expansions for the free energy and susceptibility of the two dimensional random bond ising model with a symmetric bimodal distribution of two positive coupling strengths j1 and j2 and study the influence of the quenched random bond disorder on the critical behavior of the model by analysing the series expansions over a wide range of coupling ratios j2 j1 covering the crossover from weak to strong disorder we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form t 7 4 ln t 7 8 as predicted theoretically by shalaev shankar and ludwig for the specific heat our results are less convincing but still compatible with the theoretically predicted log log singularity

exact finite size scaling corrections to the critical two dimensional ising model on a torus ii triangular and hexagonal lattices we compute the finite size corrections to the free energy internal energy and specific heat of the critical two dimensional spin 1 2 ising model on triangular and hexagonal lattices wrapped on a torus we find the general form of the finite size corrections to these quantities as well as explicit formulae for the first coefficients of each expansion we analyse the implications of these findings for the renormalization group description of the model

the three state square lattice potts antiferromagnet at zero temperature we study the 3 state square lattice potts antiferromagnet at zero temperature by a monte carlo simulation using the wang swendsen koteck cluster algorithm on lattices up to 1024 1024 we confirm the critical exponents predicted by burton and henley based on the height representation of this model

critical behaviour of an m vector spin glass for m a special case of the spin glass model is considered in which the number of spin components m becomes infinitely large the authors derive a field theory hamiltonian for this model and show that its upper critical dimensionality is eight the critical exponents for this theory are calculated in an expansion in epsilon 8 d to second order they notice that this second order expansion is identical to that for the p to infinity limit of the q3 model in epsilon 6 d

ancient numerical daemons of conceptual hydrological modeling 2 impact of time stepping schemes on model analysis and prediction 1 despite the widespread use of conceptual hydrological models in environmental research and operations they remain frequently implemented using numerically unreliable methods this paper considers the impact of the time stepping scheme on model analysis sensitivity analysis parameter optimization and markov chain monte carlo based uncertainty estimation and prediction it builds on the companion paper clark and kavetski 2010 which focused on numerical accuracy fidelity and computational efficiency empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions 1 unreliable time stepping schemes in particular fixed step explicit methods suffer from troublesome numerical artifacts that severely deform the objective function of the model these deformations are not rare isolated instances but can arise in any model structure in any catchment and under common hydroclimatic conditions 2 sensitivity analysis can be severely contaminated by numerical errors often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations 3 robust time stepping schemes generally produce better behaved objective functions free of spurious local optima and with sufficient numerical continuity to permit parameter optimization using efficient quasi newton methods when implemented within a multistart framework modern newton type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers 4 unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states 5 even when interactions between hydrological parameters and numerical errors provide the right result for the wrong reason and the calibrated model performance appears adequate unreliable time stepping schemes make the model unnecessarily fragile in predictive mode undermining validation assessments and operational use erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable especially given that robust numerics are accepted as mainstream in other areas of science and engineering we hope that the vivid empirical findings will encourage the conceptual hydrological community to close its pandora s box of numerical problems paving the way for more meaningful model application and interpretation

spanning forests and osp n 2m invariant σ models the present paper is part of our ongoing work on osp n 2m supersymmetric models their relation with the potts model at q 0 and spanning forests and the rigorous analytic continuation of the partition function as an entire function of n 2m a feature first predicted by parisi and sourlas in the 1970s here we accomplish two main steps first we analyze in detail the role of the ising variables that arise when the constraint in the osp 1 2 model is solved and we point out two situations in which the ising and forest variables decouple second we establish the analytic continuation for the osp n 2m model in some special cases when the underlying graph is a forest and for the nienhuis action on a cubic graph we also make progress in understanding the series parallel graphs

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

block cluster theory of site percolation on the four and five dimensional ordinary hypercubic lattices site percolation on the ordinary hypercubic lattice in four and five dimensions is studied using block cluster theory the exact analytic renormalisation group equations of block cluster theory are obtained by a computer algorithm they are solved numerically and yield for the susceptibility exponent gamma 1 277 d 4 gamma 1 031 d 5 and for the correlation length exponent nu 0 566 d 5

quantile hydrologic model selection and model structure deficiency assessment 2 applications quantile hydrologic model selection and structure deficiency assessment is applied in three case studies the performance of quantile model selection problem is rigorously evaluated using a model structure on the french broad river basin data set the case study shows that quantile model selection encompasses model selection strategies based on summary statistics and that it is equivalent to maximum likelihood estimation under certain likelihood functions it also shows that quantile model predictions are fairly robust the second case study is of a parsimonious hydrological model for dry land areas in western india the case study shows that an intuitive improvement in the model structure leads to reductions in asymmetric loss function values for all considered quantiles the asymmetric loss function is a quantile specific metric that is minimized to obtain a quantile specific prediction model the case study provides evidence that a quantile wise reduction in the asymmetric loss function is a robust indicator of model structure improvement finally a case study of modeling daily streamflow for the guadalupe river basin is presented a model structure that is least deficient for the study area is identified from nine different model structures based on quantile structural deficiency assessment the nine model structures differ in interception routing overland flow and base flow conceptualizations the three case studies suggest that quantile model selection and deficiency assessment provides a robust mechanism to compare deficiencies of different model structures and helps to identify better model structures in addition to its novelty quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

critical exponents for the percolation problem and the yang lee edge singularity gives details of a calculation of critical exponents for a class of field theory models that have an interaction cubic in the fields the results have already been reported give the exponents to third order in epsilon where epsilon 6 d and d is the dimensionality of space the class of models includes the percolation problem and the yang lee edge singularity so the authors give explicit results for the exponents to order epsilon 3 in these cases by resummation methods based on the symptotic behaviour of the epsilon expansion they obtain numerical estimates for these exponents for a number of interesting values of d

dynamic critical behavior of the swendsen wang algorithm the two dimensional three state potts model revisited we have performed a high precision monte carlo study of the dynamic critical behavior of the sweden wang algorithm for the two dimensional three state potts model we find that the li sokal bound int const cn is almost but not quite sharp the ratio int cn seems to diverge either as a small power 0 08 or as a logarithm

uniqueness and observability of conceptual rainfall runoff model parameters the percolation process examined many researchers have expressed concerns regarding the uniqueness of parameter estimates for conceptual rainfall runoff r r models obtained through calibration recent studies sorooshian et al this issue sorooshian and gupta this issue have revealed that even though stochastic parameter estimation techniques can help the problems are not all due to inefficiencies in the calibration techniques used but are caused by the manner in which the model is structurally formulated thus even when calibrated under ideal conditions simulation studies it is often impossible to obtain unique estimates for the parameters it is possible to resolve this problem at least in part by appropriate reparameterizations of the pertinent model equations in this paper the percolation equation of the soil moisture accounting model of the national weather service river forecast system sma nwsrfs will be discussed it is shown that a logical reparameterization of this equation can result in conditions that improve the chances of obtaining unique parameter estimates it is believed that these results have implications for other conceptual r r models in which similar approaches are used in the representation of the percolation infiltration process

conductivity exponents from the analysis of series expansions for random resistor networks there has been considerable controversy in recent years over the value of the conductivity exponent t this exponent can be deduced from series expansions via the scaling relations t zeta d 2 nu where zeta is deduced from differences between the exponents of the resistive gamma r percolative gamma p and conductive gamma c susceptibility the author finds that allowance for non analytic confluent corrections to scaling and the use of recent pc estimates leads to estimates for gamma r gamma p and gamma c that are somewhat different to those of fisch and harris 1978 however the differences between these exponents do not change significantly moreover the change in accepted estimates of nu in the last five years cancels some of this remaining discrepancy and she concludes using the relation zeta gamma r gamma p that t 1 31 d 2 t 2 04 d 3 t 2 39 d 4 t 2 72 d 5 with an error of about or 0 10 in each case the d 2 estimate is in significantly better agreement with those of other methods than that of fisch and harris

one dimensional models with 1 r2 interactions the critical behaviour of a general discrete one dimensional model with inverse square interactions is discussed using renormalisation group methods

bond percolation and the yang lee edge singularity problems in three dimensions field theories with a trilinear interaction are used to describe both the random bond percolation problem and the yang lee edge singularity problems in three dimensions at criticality renormalisation group functions are calculated to order four for the exponents eta omega and the beta function and to order five for the remaining critical exponents estimations of the critical coupling constant and the exponents for percolation theory are found by summing conformal transformations of the borel transformed series

the square lattice f model revisited a loop cluster update scaling study the six vertex f model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite order phase transition of the kosterlitz thouless type as one of the few non trivial exactly solved models it provides a welcome gauge for new numerical simulation methods and scaling techniques in view of the notorious problems of clearly resolving the kosterlitz thouless scenario in the two dimensional xy model numerically the f model in particular constitutes an instructive reference case for the simulational description of this type of phase transition we present a loop cluster update monte carlo study of the square lattice f model with a focus on the properties not exactly known such as the polarizability or the scaling dimension in the critical phase for the analysis of the simulation data finite size scaling is explicitly derived from the exact solution and plausible assumptions guided by the available exact results the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour

phase transition in the 3d random field ising model we show that the three dimensional ising model coupled to a small random magnetic field is ordered at low temperatures this means that the lower critical dimension dl for the theory isdl 2 settling a long controversy on the subject our proof is based on an exact renormalization group rg analysis of the system this analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of imry and ma the rg acts in the space of ising models and in the space of random field distributions driving the former to zero temperature and the latter to zero variance

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

lattice systems with a continuous symmetry we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

phase diagrams and cluster expansions for low temperaturep φ 2 models we give a cluster expansion for the schwinger functions of the stable phases found in part i the wightman axioms the mass gap and asymptoticity of perturbation theory follow

non self averaging in autocorrelations for potts models on quenched random gravity graphs we investigate the non self averaging properties of the dynamics of ising 4 state potts and 10 state potts models in single cluster monte carlo simulations on quenched ensembles of planar trivalent 3 random graphs which we use as an example of relevant quenched connectivity disorder we employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetization in order to discern non self averaging although the specific results discussed here are for quenched random graphs the method has quite general applicability

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

parameterizations for natural exponential families with quadratic variance functions abstract parameterizations for natural exponential families nef s with quadratic variance functions qvf s are compared according to the nearness to normality of the likelihood and posterior distribution nonnormality of the likelihood posterior is measured using two criteria the first is the magnitude of a standardized third derivative of the log likelihood logposterior density the second is a comparison of the probability of particular tail regions under the normalized likelihood posterior distribution and under the corresponding normal approximation a relationship is given that links these two criteria sample sizes are recommended for adequate normality in the likelihood for various parameterizations of the nef qvf models and these results are extended to bayesian models with a conjugate prior

asymptotic behaviour of the perturbation expansion in n 0 field theories the author develops a method for studying the high order behaviour of the perturbation expansion in theories in which the number of field components n is taken to zero this procedure is illustrated on the field theory formulation of the percolation problem which can be considered as the n 0 limit of the n 1 state potts model the saddle points controlling the asymptotic behaviour are labelled by an integer r 1 2 n for positive integer n but after continuation to n 0 the dominant contribution effectively comes from the saddle point with r infinity the perturbation expansion is found to be oscillatory at large orders and its behaviour is calculated

dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we study the dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we find that the li sokal bound on the autocorrelation time int const xc h holds along the self dual curve of the symmetric ashkin teller model and is almost but not quite sharp the ratio int c h appears to tend to infinity either as a logarithm or as a small power 0 05 p 0 12 in an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time

potts and percolation models on bowtie lattices we give the exact critical frontier of the potts model on bowtie lattices for the case of q 1 the critical frontier yields the thresholds of bond percolation on these lattices which are exactly consistent with the results given by ziff et al j phys a 39 15083 2006 for the q 2 potts model on a bowtie a lattice the critical point is in agreement with that of the ising model on this lattice which has been exactly solved furthermore we do extensive monte carlo simulations of the potts model on a bowtie a lattice with noninteger q our numerical results which are accurate up to seven significant digits are consistent with the theoretical predictions we also simulate the site percolation on a bowtie a lattice and the threshold is s c 0 5479148 7 in the simulations of bond percolation and site percolation we find that the shape dependent properties of the percolation model on a bowtie a lattice are somewhat different from those of an isotropic lattice which may be caused by the anisotropy of the lattice

rates of convergence for empirical processes of stationary mixing sequences classical empirical process theory for vapnik cervonenkis classes deals mainly with sequences of independent variables this paper extends the theory to stationary sequences of dependent variables it establishes rates of convergence for mixing and mixing empirical processes indexed by classes of functions the method of proof depends on a coupling of the dependent sequence with sequences of independent blocks to which the classical theory can be applied a uniform o ns 1 s rate of convergence over v c classes is established for sequences whose mixing coefficients decay slightly faster than o n s

ϵ expansion for the critical exponents of a vector spin glass the epsilon expansion for the critical exponents of a vector spin glass is calculated to o epsilon 3 epsilon 6 d a general cubic field theory is used

logarithmic corrections for spin glasses percolation and lee yang singularities in six dimensions we study analytically the logarithmic corrections to the critical exponents of the critical behaviour of correlation length susceptibility and specific heat for the temperature and the finite size scaling behaviour for a generic theory at its upper critical dimension six we have also computed the leading correction to scaling as a function of the lattice size we distinguish the obtained formulae to the following special cases percolation lee yang singularities and m component spin glasses we have compared our results for the ising spin glass case with numerical simulations finding a very good agreement finally and using the results obtained for the lee yang singularities in six dimensions we have computed the logarithmic corrections to the singular part of the free energy for lattice animals in eight dimensions

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

1 σ expansion for critical concentrations in the diluted spin glass the author studies the threshold concentrations pq for critical behaviour at zero temperature in the correlation functions 2q for an ising spin glass in which nearest neighbour interactions randomly assume the values j 0 and j with respective probabilities p 2 1 p and p 2 here q j sisj q av where denotes an average over the ground states for fixed configuration of j and av an average over all such configurations due to frustration effects pc p2 p4 p6 pinfinity where pc is the percolation threshold thus spin glass theory with only 2 critical at p p2 applies and the critical exponents along the t 0 axis are the same as thermal critical exponents for p 1 when the values j and j are replaced by distributions of narrow width the frustration is removed and percolation exponents are expected at p pc

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

quantile hydrologic model selection and model structure deficiency assessment 1 theory a theory for quantile based hydrologic model selection and model structure deficiency assessment is presented the paper demonstrates that the degree to which a model selection problem is constrained by the model structure measured by the lagrange multipliers of the constraints quantifies structural deficiency this leads to a formal definition of model structure deficiency or rigidity model structure deficiency introduces a bias in the prediction of an observed quantile which is often not equal across quantiles structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing the analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles in addition to such novelties quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

quantum chaos an entropy approach a new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics it generalizes other definitions of entropy in both the classical and quantum cases the kolmogorov sinai ks entropy is obtained for a classical system and the sharp measurement instrument for a quantum system and a coherent states instrument a new quantity coherent states entropy is defined it may be used to measure chaos in quantum mechanics the following correspondence principle is proved the upper limit of the coherent states entropy of a quantum map as 0 is less than or equal to the ks entropy of the corresponding classical map chaos umpire sits and by decision more imbroils the fray by which he reigns next him high arbiter chance governs all john milton paradise lost book ii

scaling relations for logarithmic corrections multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical mechanical systems here a lee yang zero approach is used to systematically analyze the exponents of such logarithms and to propose scaling relations between them these proposed relations are then confronted with a variety of results from the literature

directed lattice animals and the lee yang edge singularity the exponents nu perpendicular to gamma of directed animals in d dimensions are shown to equal those for the lee yang problem in d 1 dimensions for d 2 the author obtains the exact results nu perpendicular to theta 1 2 and for d or 7 the scaling relation theta d 1 nu perpendicular to

the number of link and cluster states the core of the 2d q state potts model due to fortuin and kastelyin the q state potts model has a representation as a sum over random graphs generalizing the potts model to arbitrary q is based on this representation a key element of the random cluster representation is the combinatorial factor which is the number of ways to form distinct clusters consisting of totally edges we have devised a method to calculate from monte carlo simulations

critical and off critical conformal analysis of the ising quantum chain in an imaginary field the critical curve with central charge c 22 5 of the ising quantum chain in an imaginary longitudinal field is calculated by finite size extrapolation of the yang lee square root branch point position various power laws are found the field dependence of the off criticality mass scale and the four lowest off criticality scaling functions are calculated the latter turn out to be universal along the critical line and agree very well with the results of the truncated hilbert space method for the c 22 5 continuum theory the author obtains the universal bulk scaling coefficient in qualitative agreement with the thermodynamic bethe ansatz result the scattering phaseshift calculated by luscher s method 1988 reproduces the cardy mussardo minimal solution 1989 for the s matrix if a boundary defect is introduced the only non trivial primary field decouples so that the spectrum consists only of the tower of the unit operator in the antiferromagnetic regime with a non staggered imaginary field the author finds boundary dependent lines where the gap vanishes

renormalization group theory for cooling first order phase transitions in potts models we develop a dynamic field theoretic renormalization group rg theory for cooling first order phase transitions in the potts model it is suggested that the well known imaginary fixed points of the q state potts model for q 10 3 in the rg theory are the origin of the dynamic scaling found recently from numerical simulations apart from logarithmic corrections this indicates that the real and imaginary fixed points of the potts model are both physical and control the scalings of the continuous and discontinuous phase transitions respectively of the model our one loop results for the scaling exponents are already not far away from the numerical results further the scaling exponents depend on q only slightly consistent with the numerical results therefore the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first order phase transition of the potts model

running wave solutions of the two dimensional sine gordon equation after the lamb substitution the 2d sine gordon equation was solved three classes of solutions for this equation were found ad hoc the 2d sine gordon equation was reduced to an algebraic system consisting of three equations the solutions given of the 2d sine gordon equation are a generalization of the solutions of the 1d sine gordon equation they are also a generalization of the solutions of the equation phi xx yy sin phi x y

antiferromagnetic potts models on the square lattice a high precision monte carlo study we study the antiferromagnetic q state potts model on the square lattice for q 3 and q 4 using the wang swendsen koteck wsk monte carlo algorithm and a powerful finite size scaling extrapolation method for q 3 we obtain good control up to correlation length 5000 the data are consistent with ae2 p 1 a1e as with p 1 the staggered susceptibility behaves as stagg 5 3 for q 4 the model is disordered 2 even at zero temperature in appendices we prove a correlation inequality for potts antiferromagnets on a bipartite lattice and we prove ergodicity of the wsk algorithm at zero temperature for potts antiferromagnets on a bipartite lattice

microcanonical finite size scaling in second order phase transitions with diverging specific heat a microcanonical finite size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so called quotients method to the microcanonical ensemble the ansatz is tested numerically in two models where the canonical specific heat diverges at criticality thus implying fisher renormalization of the critical exponents the three dimensional ferromagnetic ising model and the two dimensional four state potts model where large logarithmic corrections are known to occur in the canonical ensemble a recently proposed microcanonical cluster method allows simulating systems as large as l 1024 potts or l 128 ising the quotients method provides accurate determinations of the anomalous dimension ensuremath eta and of the fisher renormalized thermal ensuremath nu exponent while in the ising model the numerical agreement with our theoretical expectations is very good in the potts case we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data

percolation of the site random cluster model by monte carlo method we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation to simulate the model on a square lattice we combine the color assignation and the swendsen wang methods to design a highly efficient cluster algorithm with a small critical slowing down phenomenon to verify whether or not it is consistent with the bond random cluster model we measure several quantities such as the wrapping probability re the percolating cluster density p and the magnetic susceptibility per site p as well as two exponents such as the thermal exponent yt and the fractal dimension yh of the percolating cluster we find that for different exponents of cluster weight q 1 5 2 2 5 3 3 5 and 4 the numerical estimation of the exponents yt and yh are consistent with the theoretical values the universalities of the site random cluster model and the bond random cluster model are completely identical for larger values of q we find obvious signatures of the first order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site our results are helpful for the understanding of the percolation of traditional statistical models

dynamic critical behavior of the chayes machta algorithm for the random cluster model i two dimensions we study via monte carlo simulation the dynamic critical behavior of the chayes machta dynamics for the fortuin kasteleyn random cluster model which generalizes the swendsen wang dynamics for the q state potts ferromagnet to non integer q 1 we consider spatial dimension d 2 and 1 25 q 4 in steps of 0 25 on lattices up to 10242 and obtain estimates for the dynamic critical exponent z cm we present evidence that when 1 q 1 95 the ossola sokal conjecture z cm is violated though we also present plausible fits compatible with this conjecture we show that the li sokal bound z cm is close to being sharp over the entire range 1 q 4 but is probably non sharp by a power as a byproduct of our work we also obtain evidence concerning the corrections to scaling in static observables

simulations of lattice animals and trees the scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions using as microscopic models lattice animals and lattice trees on simple hypercubic lattices as a stochastic sampling method we use a biased sequential sampling algorithm with re sampling similar to the pruned enriched rosenbluth method perm used extensively for linear polymers essentially we start simulating percolation clusters either site or bond re weigh them according to the animal tree ensemble and prune or branch the further growth according to a heuristic fitness function in contrast to previous applications of perm this fitness function is not the weight with which the actual configuration would contribute to the partition sum but is closely related to it we obtain high statistics of animals with up to several thousand sites in all dimension 2 d 9 in addition to the partition sum number of different animals we estimate gyration radii and numbers of perimeter sites in all dimensions we verify the parisi sourlas prediction and we verify all exactly known critical exponents in dimensions 2 3 4 and 8 in addition we present the hitherto most precise estimates for growth constants in d 3 for clusters with one site attached to an attractive surface we verify for d 3 the superuniversality of the cross over exponent at the adsorption transition predicted by janssen and lyssy but not for d 2 there we find 0 480 4 instead of the conjectured 1 2 finally we discuss the collapse of animals and trees arguing that our present version of the algorithm is also efficient for some of the models studied in this context but showing that it is not very efficient for the classical model for collapsing animals