spectral asymptotics for the third order operator with periodic coefficients abstract we consider the self adjoint third order operator with 1 periodic coefficients on the real line the spectrum of the operator is absolutely continuous and covers the real line we determine the high energy asymptotics of the periodic antiperiodic eigenvalues and of the branch points of the lyapunov function furthermore in the case of small coefficients we show that either whole spectrum has multiplicity one or the spectrum has multiplicity one except for a small spectral nonempty interval with multiplicity three in the last case the asymptotics of this small interval is determined

evolution of the universality class in slightly diluted 1 p 0 8 ising systems the crossover of a pure undiluted ising system spin per site probability p 1 to a diluted ising system spin per site probability p 0 8 is studied by means of monte carlo calculations with p ranging between 1 and 0 8 at intervals of 0 025 the evolution of the self averaging is analyzed by direct determination of the normalized square widths rm and r as a function of p we find a monotonous and smooth evolution from the pure to the randomly diluted universality class the p dependent transition is found to be indepent of size l this property is very convenient for extrapolation towards the randomly diluted universality class avoiding complications resulting from finite size effects

monte carlo renormalization of the three dimensional ising model abstract we have investigated the simple cubic ising model by means of the monte carlo renormalization technique the emphasis of our study concerns the influence of truncation i e the dimensionality of the coupling subspace in which the analysis of the correlation functions generated by the monte carlo and spin blocking algorithms is performed to this purpose we have included up to 36 even and 21 odd couplings in our analysis we find that the increase in the number of couplings has a significant influence on the largest eigenvalues of the linearized renormalization transformation matrices these eigenvalues serve to estimate the renormalization exponents yi and yh remarkably we find no significant finite size effect on these eigenvalues when the maximum number of couplings is included in the analysis except for the smallest system sizes 83 43 after a suitable extrapolation to the fixed point we find good agreement with existing results for the critical exponents we have determined the critical point of the simple cubic ising model as k 0 221652 6 also in agreement with existing results

random cluster representation for the blume capel model we present in this paper a way to perform the mapping of the spin 1 blume capel model into a random cluster model and analyze thermodynamic properties of the former model in terms of geometric properties of clusters generated in the random cluster representation it is shown that there are two different relevant types of cluster and that one of them is the exact analogue of the type of cluster generated in the ising model we use this result to derive expressions for thermodynamical properties on the second order transition line which are equivalent to the ones found in the ising model the other type of cluster is responsible for the first order transitions and we may see the tricritical point as a point where both types of cluster compete on the same footing

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

critical finite size scaling of magnetization distribution function for baxter wu model abstract the distribution function pl m of the order parameter for the baxter wu model is studied using blocks of linear dimension l of a larger triangular lattice at a given temperature we use the metropolis algorithm for the generation of a sample of configurations on the triangular lattice the similarities and differences of this distribution with the usual cases of ising lattices are investigated we conclude that the present model obeys at the critical temperature a finite scaling law with the known critical exponents as expected however our numerical data strongly indicate that the analytic form of the scaling function does not conform to the corresponding function for the usual ising model an analytic expression that gives a good fit is presented

extended scaling functions for ising systems with dimensionality 1 d 4 abstract finite size lattice monte carlo simulations of phase transitions in ising systems 1 d 4 allow the determination of simple binomial scaling functions for t t c and t t c consistent with the asymptotic behavior for the critical isotherm the spontaneous magnetization and the zero field susceptibility which describe quite well the scaling behavior in an extended range of the scaling variable 0 01 t t c t c l 1 20 for all four dimensionalities

computing the roughening transition of ising and solid on solid models by bcsos model matching we study the roughening transition of the dual of the two dimensional 2d xy model of the discrete gaussian model of the absolute value solid on solid model and of the interface in an ising model on a three dimensional 3d simple cubic lattice the investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago the basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body centred solid on solid bcsos model our estimates for the critical couplings are and for the xy model the discrete gaussian model and the absolute value solid on solid model respectively for the inverse roughening temperature of the ising interface we find to the best of our knowledge these are the most precise estimates for these parameters published so far

asymmetric fluid criticality ii finite size scaling for simulations the vapor liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions l focusing on periodic boundary conditions as appropriate for simulations the recently propounded complete thermodynamic stackrel ensuremath rightarrow l ensuremath infty scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling phys rev e 67 061506 2003 is extended to finite l initially in a grand canonical representation the theory allows for a yang yang anomaly in which when stackrel ensuremath rightarrow l ensuremath infty the second temperature derivative d 2 ensuremath mu ensuremath sigma dt 2 of the chemical potential along the phase boundary ensuremath mu ensuremath sigma t diverges when stackrel ensuremath rightarrow t t mathrm c ensuremath the finite size behavior of various special critical loci in the temperature density or t ensuremath rho plane in particular the k inflection susceptibility loci and the q maximal loci derived from q l t ensuremath rho l ensuremath equiv m 2 l 2 m 4 l where m ensuremath equiv ensuremath rho ensuremath ensuremath rho l is carefully elucidated and shown to be of value in estimating t mathrm c and ensuremath rho mathrm c concrete illustrations are presented for the hard core square well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent ensuremath nu that confirms ising type character the treatment is extended to the canonical representation where further complications appear

accurate estimates of 3d ising critical exponents using the coherent anomaly method abstract an analysis of the critical behavior of the three dimensional ising model using the coherent anomaly method cam is presented various sources of errors in cam estimates of critical exponents are discussed and an improved scheme for the cam data analysis is tested using a set of mean field type approximations based on the variational series expansion approach accuracy comparable to the most precise conventional methods has been achieved our results for the critical exponents are given by 0 108 5 0 327 4 1 237 4 and 4 77 5

partition function zeros and leading order scaling correction of the 3d ising model from multicanonical simulations the density of states for the three dimensional ising model is calculated with high precision by means of multicanonical simulations this allows us to estimate the leading partition function zeros for lattice sizes up to l 32 we have evaluated the critical exponent and the correction to scaling through an analysis of a multi parameter fit and of the bulirsch stoer bst extrapolation algorithm the performance of the bst algorithm is also explored in case of the 2d ising model where the exact partition function zeros are known

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

dynamical effects of loss of cooperation in discrete time hypercycles abstract hypercycles dynamics have been widely investigated in the context of origins of life especially using time continuous dynamical models different hypercycle architectures jeopardising their stability and persistence have been discussed and investigated namely the catalytic parasites and the short circuits here we address a different scenario considering rna based hypercycles in which cooperation is lost and catalysis shifts to density dependent degradation processes due to the acquisition of cleaving activity by one hypercycle species that is we study the dynamical changes introduced by a functional shift to do so we use a discrete time model that can be approached to the time continuous limit by means of a temporal discretisation parameter labelled c we explore dynamical changes tied to the loss of cooperation in two three and four member hypercycles in this discrete time setting with cooperation the all species coexistence in two and three member hypercycles is governed by an internal stable fixed point when one species shifts to directed degradation a transcritical bifurcation takes place and the other hypercycle members go to extinction the asymptotic dynamics of the four member system is governed by an invariant curve in its cooperative regime for this system we have identified a simultaneous degenerate transcritical neimark sacker bifurcation as cooperation switches to directed degradation after these bifurcations as we found for the other systems all the cooperative species except the one performing degradation become extinct finally we also found that the observed bifurcations and asymptotic dynamical behaviours are independent of c our results can help in understanding the impact of changes in ecological interactions i e functional shifts in multi species systems and to determine the nature of the transitions tied to co extinctions and out competition processes in both ecosystems and rna based systems

transfer matrix test of the two cell mean field renormalization group abstract a transfer matrix approach has been worked out to test the predictions of the two cell mean field renormalization group mfrg for the square ising cells with linear size up to l 11 the convergence of the finite size critical couplings towards the exact value both for mfrg and for the cluster mfa is shown and the limit of the ratio yh yt consistent with the corresponding universal value is found applications within mfa are also briefly discussed

time averages for heteroclinic attractors in neighbourhoods of attracting heteroclinic cycles the time averages fail to converge for almost all initial conditions but spiral closer and closer to the boundary of a polygon this is shown by using a poincare section argument

high temperature series for scalar field lattice models generation and analysis an implementation of the free embedding scheme for high temperature series generation on the body centered cubic family of lattices in arbitrary dimensiond is described series to order 21 in inverse temperature are tabulated for several scalar field models both for the magnetic susceptibility and for the second moment of the spin correlation function the critical behavior of a family of 3 dimensional double gaussian models which interpolate continuously between the spin 1 2 ising model and the gaussian model is analyzed in detail away from the gaussian model limit using confluent inhomogeneous secondorder differential approximants with our best estimate of the correction to scaling exponent 0 52 0 03 the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by 1 237 0 002 and 0 630 0 0015 respectively and 2 0 0359 0 0007

interpolation parameter and expansion for a three dimensional nontrivial scalar infrared fixed point we compute a nontrivial infrared 34 fixed point by means of an interpolation expansion in fixed dimension the expansion is formulated for an infinitesimal momentum space renormalization group we choose a coordinate representation for the fixed point interaction in derivative expansion and compute its coordinates to high orders by means of computer algebra we compute the series for the critical exponentv up to order 25 of interpolation expansion in this representation and evaluate it using pade borel pade borel conformal pade andd log pade resummation the resummation returns 0 6262 13 as the value ofv our renormalization group uses canonical resealing for which 0

on a riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non selfadjoint problem deduced from a perturbation method for sound radiation in the present paper we prove that the family of exponentials associated to the eigenvalues of the perturbed operator t t0 t1 2t2 ktk forms a riesz basis in l2 0 t t 0 where c t0 is a closed densely defined linear operator on a separable hilbert space h with domain d t0 having isolated eigenvalues with multiplicity one while t1 t2 are linear operators on h having the same domain d d t0 and satisfying a specific growing inequality after that we generalize this result using a h lipschitz function as application we consider a non selfadjoint problem deduced from a perturbation method for sound radiation

finite size calculations on the three dimensional ising model abstract recent numerical results for the critical behaviour of the three dimensional ising model based on finite size calculations show significant discrepancies we review possible sources of systematic deviations and strategies to avoid these or to track them down we present some new finite size results for the binder cumulant obtained by means of a perturbation expansion and by cluster monte carlo methods

monte carlo investigations of phase transitions status and perspectives abstract using the concept of finite size scaling monte carlo calculations of various models have become a very useful tool for the study of critical phenomena with the system linear dimension as a variable as an example several recent studies of ising models are discussed as well as the extension to models of polymer mixtures and solutions it is shown that using appropriate cluster algorithms even the scaling functions describing the crossover from the ising universality class to the mean field behavior with increasing interaction range can be described additionally the issue of finite size scaling in ising models above the marginal dimension d 4 is discussed

a monte carlo study of leading order scaling corrections of phi 4 theory on a three dimensional lattice we present a monte carlo study of the one component 4 model on a cubic lattice in three dimensions leading order scaling corrections are studied using the finite size scaling method we compute the corrections to scaling exponent with high precision we determine the value of the coupling at which leading order corrections to scaling vanish using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods

amplitude ratios for critical systems in the c 2 universality class we study the finite size corrections of the critical dense polymer cdp and the dimer models on n rectangular lattice we find that the finite size corrections in the cdp and dimer models depend in a crucial way on the parity of n and a change of the parity of n is equivalent to the change of boundary conditions we present a set of universal amplitude ratios for amplitudes in finite size correction terms of critical systems in the universality class with central charge c 2 the results are in perfect agreement with a perturbated conformal field theory under the assumption that all analytical corrections coming from the operators which belongs to the tower of the identity our results inspire many interesting problems for further studies

on the combinatorial solution of the ising model an attempt to generalise the combinatorial solution of the two dimensional 2d nearest neighbour nn ising model to three dimensions is reported a generating function which fully exposes the symmetry of the lattice is derived for the 2d square ising model a natural extension to the 3d simple cubic sc lattice is shown to be false a certain circumstance for the 2d case leads to the conjecture that tanh j ktc square root 5 2 cos pi 8 for the scnn ising model

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

finite size scaling of the three dimensional conserved order parameter ising model via wang landau algorithm abstract the critical properties of the conserved order parameter cop version of the three dimensional ising model with zero magnetization were investigated by means of the monte carlo mc wang landau algorithm the study was carried out in appropriate restricted but dominant energy subspaces the main effort was focused on the specific heat and binder energy cumulant by using the density of states of the model for lattices with linear size l 4 60 by applying finite size scaling analysis the estimated values for the thermal critical exponent y t and critical temperature k c are in agreement with the considered as best values leading to the conclusion that this model belongs to the ising universality class the analysis revealed the necessity of corrections to scaling functions for interpreting correctly the mc data

a special purpose processor for the monte carlo simulation of ising spin systems a description is given of a special purpose computer for the study of static and dynamic properties of stochastic ising like systems of up to 4 106 spins elementary monte carlo steps are executed in the machine at a rate of 1 5 mhz the first results are given obtained as part of a testing procedure of the machine

critical temperature of the ising ferromagnet on the fcc hcp and dhcp lattices abstract by an extensive monte carlo calculation together with the finite size scaling and the multiple histogram method the critical coupling constant k c j k b t c of the ising ferromagnet on the fcc hcp and double hcp dhcp lattices were obtained with unprecedented precision k c fcc 0 1020707 2 k c hcp 0 1020702 1 and k c dhcp 0 1020706 2 the critical temperature t c of the hcp lattice is found to be higher than those of the fcc and the dhcp lattice the dhcp lattice seems to have higher t c than the fcc lattice but the difference is within error bars

a difference equation model for the hypercycle the paper presents a qualitative analysis of a system of n cyclically coupled difference equations x i x i c k i x i 1 c phi 1 with phi sum k i x i x i 1 which may be viewed as a discrete analogue of the hypercycle differential equation dot x i x i k i x i 1 phi these equations are of particular interest in the theory of self organization and biological evolution and have applications to the study of the social behaviour of animals

monte carlo analysis of the extended ashkin teller model abstract monte carlo simulations are used to analyse the behavior of the extended ashkin teller model in two dimensions from the ratio of the square of the second moment of the order parameter to its fourth moment the critical surface in three dimensional parameter space is calculated in regions where the ising transitions are expected the continuity of the order parameter at the critical surface is verified by a finite size scaling analysis for both ferromagnetic and antiferromagnetic parts of the phase diagram

smooth finite size behaviour of the three dimensional ising model abstract we have obtained monte carlo results for finite simple cubic ising models at criticality the susceptibility data are consistent with a smooth approach to the asymptotic behaviour for large system sizes

computer simulation studies of critical phenomena abstract the recent strides which have been made in the use of computer simulations to study phase transitions and critical phenomena are reviewed we describe how the use of a combination of recently developed histogram techniques and sophisticated monte carlo simulation algorithms have allowed the determination of the static critical behavior of the d 3 ising and heisenberg models with unprecedented precision we also discuss the study of dynamic critical behavior in simple spin models by both monte carlo and spin dynamics methods recent estimates for dynamic critical exponents are reviewed including the first high precision estimate for true dynamics

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

analysis of quasi dynamic ordinary differential equations and the quasi dynamic replicator abstract we study the mathematical properties of the quasi dynamic ordinary differential equations defined empirically in chen et al 2019 in particular we show how the allometric scaling mentioned in that work emerges naturally from the generalized lotka volterra model under the quasi dynamic ordinary differential equations paradigm we then define and study the proportional quasi dynamic ordinary differential equations and discuss the relationship of this equation system to both the classical and discrete time replicator dynamics we prove asymptotic properties of these systems for large and small populations and show that there exist populations for which the proportion of the population varies cyclically as a function of total logarithmic population size

on an riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid abstract in this paper we prove that the system of generalized eigenvectors of the operator i ek 1d4 dx4 forms a riesz basis of l2 l l where k is the integral operator with kernel the hankel function of the first kind and order 0 this operator was introduced in j sound vibration 177 1994 259 275 we give positive answers to the hypotheses posed in that article

critical structure factor in ising systems we perform a large scale monte carlo simulation of the three dimensional ising model on simple cubic lattices of size l 3 with l 128 and 256 we determine the corresponding structure factor fourier transform of the two point function and compare it with several approximations and with experimental results we also compute the turbidity as a function of the momentum of the incoming radiation focusing in particular on the deviations from the ornstein zernike expression of puglielli and ford

verification of ising phase transitions in the three dimensional ashkin teller model using monte carlo simulations monte carlo simulations in the three dimensional 3d ashkin teller model on a cubic lattice are performed in the regions of the two parameter space diagram where ising type phase transitions are expected the scaling behavior of the binder cumulant q and the magnetic susceptibility in the critical region are exploited in simulations the periodic boundary conditions and the metropolis algorithm are used starting from ising critical exponents and applying the finite size scaling analysis of the cumulant q with nonlinear corrections the accurate positions of the critical couplings on the continuous phase transition lines are calculated for these couplings the critical exponent y h is calculated analyzing the magnetic susceptibility in the framework of the finite size scaling with corrections the values of y h agree with the 3d ising model value along two lines determined by the order parameter ssigma

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

scaling properties of the baxter wu model abstract we use a recently developed cluster algorithm for the baxter wu model to study characteristic features of its behavior magnetic scaling properties of the model are investigated for second order phase transitions we improve significantly the accuracy of monte carlo simulation results and we provide new results for the behavior of the binder cumulants for temperatures below above and at the critical point

percolation between vacancies in the two dimensional blume capel model using suitable monte carlo methods and finite size scaling we investigate the blume capel model on the square lattice we construct percolation clusters by placing nearest neighbor bonds between vacancies with a variable bond probability pb at the tricritical point we locate the percolation threshold of these vacancy clusters at pbc 0 706 336 at this point we determine the fractal dimension of the vacancy clusters as xf 0 13085 21 160 and the exponent governing the renormalization flow in the pb direction as yp 0 4262 17 40 for bond probability pbpbc the vacancy clusters maintain strong critical correlations the fractal dimension is xf 0 07502 3 40 and the leading correction exponent is yp 0 452 19 40 the above values fit well in the kac table for the tricritical ising model these vacancy clusters have much analogy with those consisting of ising spins of the same sign although the associated quantities and magnetization m are energylike and magnetic quantities respectively however along the critical line of the blume capel model the vacancies are more or less uniformly distributed over the whole lattice in this case no critical percolation correlations are observed in the vacancy clusters at least in the physical region pb 1

dynamical behaviors determined by the lyapunov function in competitive lotka volterra systems dynamical behaviors of the competitive lotka volterra system even for 3 species are not fully understood in this paper we study this problem from the perspective of the lyapunov function we construct explicitly the lyapunov function using three examples of the competitive lotka volterra system for the whole state space 1 the general 2 species case 2 a 3 species model and 3 the model of may leonard the basins of attraction for these examples are demonstrated including cases with bistability and cyclical behavior the first two examples are the generalized gradient system where the energy dissipation may not follow the gradient of the lyapunov function in addition under a new type of stochastic interpretation the lyapunov function also leads to the boltzmann gibbs distribution on the final steady state when multiplicative noise is added

evolutionary dynamics of populations with conflicting interactions classification and analytical treatment considering asymmetry and power evolutionary game theory has been successfully used to investigate the dynamics of systems in which many entities have competitive interactions from a physics point of view it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur be it spins particles bacteria animals or humans here we analyze the case where the entities are heterogeneous particularly the case of two populations with conflicting interactions and two possible states for such systems explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues which determine their stability in this way four different types of system dynamics can be classified and the various kinds of phase transitions between them will be discussed while these results are interesting from a physics point of view they are also relevant for social economic and biological systems as they allow one to understand conditions for 1 the breakdown of cooperation 2 the coexistence of different behaviors subcultures 3 the evolution of commonly shared behaviors norms and 4 the occurrence of polarization or conflict we point out that norms have a similar function in social systems that forces have in physics

full characterization of a strange attractor chaotic dynamics in low dimensional replicator system abstract two chaotic attractors observed in lotka volterra equations of dimension n 3 are shown to represent two different cross sections of one and the same chaotic regime the strange attractor is studied in the equivalent four dimensional catalytic replicator network analytical expressions are derived for the lyapunov exponents of the flow in the centre of the chaotic regime the strange attractor was characterized by the lyapunov dimension dl 2 06 0 02 and the renyi fractal dimensions the set corresponding to the attractor represents a multifractal its singularity spectrum is computed one route in parameter space leading into the chaotic regime and crossing it was studied in detail it leads to a feigenbaum type cascade of bifurcations before the chaos is fully developed the dynamic system passes an internal crisis through a period two tangent bifurcation then a second sequence of period doubling bifurcations leading to another chaotic regime is observed which eventually ends in a crisis and then after a rather complicated periodic regime the attractor finally disappears trajectories in the intermediate periodic regime show transient chaotic bursts of intermittency type a series of one dimensional maps is derived from a properly chosen poincare cross section which illustrates structural changes in the attractor mutations are included in the catalytic replicator network and the changes in the dynamics observed are compared with the predictions of an approach based on perturbation theory the most striking result is the gradual disappearance of complex dynamics with increasing mutation rates the parameter space spanned by the mutation rate and selected parameters of the replication network is split in regions of complex periodic behaviour near the chaotic regime fractal boundaries of these regions are likely to occur but the data available do not allow definitive conclusions yet

cluster monte carlo simulation of the transverse ising model we formulate a cluster monte carlo method for the anisotropic limit of ising models on d 1 dimensional lattices which in effect are equivalent with d dimensional quantum transverse ising models using this technique we investigate the transverse ising models on the square triangular kagome honeycomb and simple cubic lattices the monte carlo data are analyzed by finite size scaling in each case we find as expected that the critical behavior fits well in the d 1 dimensional ising universality class for the transverse ising model on the square lattice we determine the binder cumulant of the classical counterpart for a range of aspect ratios between the system sizes in the third or classical direction and that in the other two directions matching this universal function with the case of the isotropic ising model yields the length ratio relating the isotropic ising model with the anisotropic limit the efficiency of the present algorithm is reflected by the precision of its results which improves significantly on earlier analyses

high dimensional lattice gases we investigate the critical behaviour of hard core lattice gases in four five and six dimensions by means of monte carlo simulations in order to suppress critical slowing down we use a geometrical cluster monte carlo algorithm in particular nearest neighbour exclusion lattice gases on simple hypercubic lattices are investigated these models undergo ising like ordering transitions where the majority of the lattice gas particles settle on one of two sublattices a finite size scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour the results agree with the renormalization predictions at and above the upper critical dimensionality in particular the predicted value of the binder cumulant is confirmed

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

analytical methods for recovering coefficients in differential equations from spectral data in this paper analytical methods for recovering coefficients from spectral data are discussed properties of these methods are given and mathematical models for which these methods might apply are presented

numerical solutions of a three competition lotka volterra system abstract this paper is concerned with finite difference solutions of a lotka volterra reaction diffusion system with three competing species the reaction diffusion system is discretized by the finite difference method and the investigation is devoted to the finite difference system for the time dependent solution and its asymptotic behavior in relation to the corresponding steady state problem three monotone iterative schemes for the computation of the time dependent solution are presented and the sequences of iterations are shown to converge monotonically to a unique positive solution also discussed is the asymptotic behavior of the time dependent solution in relation to various steady state solutions a simple condition on the competing rate constants is obtained which ensures that for every nontrivial nonnegative initial function the corresponding time dependent solution converges either to a unique positive steady state solution or to one of the semitrivial steady state solutions the above results lead to the coexistence and permanence of the competing system as well as computational algorithms for numerical solutions some numerical results from these computational algorithms are given all the conclusions for the reaction diffusion equations are directly applicable to the finite difference solution of the corresponding ordinary differential system

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

scaling corrections site percolation and ising model in three dimensions using finite size scaling techniques we obtain accurate results for critical quantities of the ising model and the site percolation in three dimensions we pay special attention to parametrizing the corrections to scaling which is necessary to bring the systematic errors below the statistical ones

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

universality of the ising and the s 1 model on archimedean lattices a monte carlo determination the ising models s 1 2 and s 1 are studied by efficient monte carlo schemes on the 3 4 6 4 and the 3 3 3 3 6 archimedean lattices the algorithms used a hybrid metropolis wolff algorithm and a parallel tempering protocol are briefly described and compared with the simple metropolis algorithm accurate monte carlo data are produced at the exact critical temperatures of the ising model for these lattices their finite size analysis provide with high accuracy all critical exponents which as expected are the same with the well known 2d ising model exact values a detailed finite size scaling analysis of our monte carlo data for the s 1 model on the same lattices provides very clear evidence that this model obeys also very well the 2d ising model critical exponents as a result we find that recent monte carlo simulations and attempts to define effective dimensionality for the s 1 model on these lattices are misleading accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two archimedean lattices

diversity of critical behavior within a universality class we study spatial anisotropy effects on the bulk and finite size critical behavior of the mathrm o n symmetric anisotropic ensuremath varphi 4 lattice model with periodic boundary conditions in a d dimensional hypercubic geometry above at and below t c the absence of two scale factor universality is discussed for the bulk order parameter correlation function the bulk scattering intensity and for several universal bulk amplitude relations the anisotropy parameters are observable by scattering experiments at t c for the confined system renormalization group theory within the minimal subtraction scheme at fixed dimension d for 2ldl4 is employed in contrast to the ensuremath epsilon 4 ensuremath d expansion the fixed d finite size approach keeps the exponential form of the order parameter distribution function unexpanded for the case of cubic symmetry and for n 1 our perturbation approach yields excellent agreement with the monte carlo mc data for the finite size amplitude of the free energy of the three dimensional ising model at t c by mon phys rev lett 54 2671 1985 the ensuremath epsilon expansion result is in less good agreement below t c a minimum of the scaling function of the excess free energy is found we predict a measurable dependence of this minimum on the anisotropy parameters the relative anisotropy effect on the free energy is predicted to be significantly larger than that on the binder cumulant our theory agrees quantitatively with the nonmonotonic dependence of the binder cumulant on the ferromagnetic next nearest neighbor nnn coupling of the two dimensional ising model found by mc simulations of selke and shchur j phys a 38 l739 2005 our theory also predicts a nonmonotonic dependence for small values of the antiferromagnetic nnn coupling and the existence of a lifshitz point at a larger value of this coupling the nonuniversal anisotropy effects in the finite size scaling regime are predicted to satisfy a kind of restricted universality the tails of the large l behavior at t ensuremath ne t c violate both finite size scaling and universality even for isotropic systems as they depend on the bare four point coupling of the ensuremath varphi 4 theory on the cutoff procedure and on subleading long range interactions

two limit cycles in three dimensional lotka volterra systems abstract among the six classes of zeeman s classification for three dimensional lotka volterra competitive systems with limit cycles besides the heteroclinic cycle case case 27 we construct in three cases without heteroclinic cycle cases 26 28 29 two limit cycles our construction gives a partial answer to hofbauer and so s problem to these systems

comparison between finite size field theory and monte carlo simulations for the three dimensional ising model abstract recent field theoretic predictions of finite size effects for various thermodynamic quantities near the critical point are compared with new accurate monte carlo mc data for the l l l ising model obtained from a cluster algorithm special purpose computer owing to the large size l 32 64 128 256 of the ising models these mc data permit to test the finite size field theory in the asymptotic scaling region above and below t c the results constitute the most accurate confirmation of finite size scaling in three dimensions obtained to date in a wide range of temperatures agreement with the predicted shape of the finite size scaling functions is found on a quantitative level

cluster dynamics and universality of ising lattice gases abstract lattice gases with nearest neighbour exclusion are studied by means of monte carlo simulations with an efficient cluster algorithm the critical dynamics is consistent with a dynamical exponent z 0 in the case of wolff like cluster updates for square and simple cubic lattices in the studied range of lattice sizes we find the critical activity z c 0 72020 4 for the body centred cubic lattice the critical exponents y h 2 475 8 and y t 1 61 6 disagree with an earlier study but they do agree with the known values for the three dimensional ising universality class

automatic search for multiple limit cycles in three dimensional lotka volterra competitive systems with classes 30 and 31 in zeeman s classification abstract among the six classes of zeeman s classification for three dimensional lotka volterra competitive systems with limit cycles besides the classes 26 27 28 and 29 multiple limit cycles are found in classes 30 and 31 by an algorithmic method proposed by hofbauer and so j hofbauer j w so multiple limit cycles for three dimensional lotka volterra equations appl math lett 7 1994 65 70 this also gives an answer to a problem proposed in j hofbauer j w so multiple limit cycles for three dimensional lotka volterra equations appl math lett 7 1994 65 70

uniqueness for near constant data in fourth order inverse eigenvalue problems abstract let l p u d4u dx4 d dx p1 du dx p2u u 0 u 0 u 1 u 1 0 where p l2 0 1 l2 0 1 we show that for near constant coefficients if p is even about 1 2 and l p and l p have the same eigenvalues then knowledge of the first coefficient uniquely determines the second up to average value further we show that knowledge of the second coefficient uniquely determines the first we derive precise eigenfunction asymptotics using resolvent perturbation theory and prove the result using a simple perturbation of basis argument

on the riesz basis of a family of analytic operators in the sense of kato and application to the problem of radiation of a vibrating structure in a light fluid abstract in this paper we prove that the system formed by some of generalized eigenvectors of the operator t 0 e t 1 e 2 t 2 which are analytic on e forms a riesz basis of the separable hilbert space h where e c and t 0 t 1 t 2 some linear transformations on h which have the same domain d h after that we give an application for a problem concerning the radiation of a vibrating structure in a light fluid

confluent singularities in 3d continuum φ4 theory resolving critical point discrepancies a new analysis of the three dimensional 4 continuum model series for critical exponents and amplitude ratios is presented by explicitly allowing for a second correction to scaling term with exponent 2 and 2 1 2 0 a revision is found of previous critical point estimates that are all in the direction of resolving the remaining discrepancies between the 3d and 4 analyses the new estimates are also consistent with those obtained from high temperature series analyses of 3d lattice ising models for example the exponents 1 238 0 630 0 0355 and correction to scaling amplitude ratio 0 77 are easily accommodated and possibly even preferred detailed verification will require further terms both in the low order perturbation theory and the high order asymptotic expansions