conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

boundary susceptibility in the open xxz chain in the first part we calculate the boundary susceptibility b in the open xxz chain at zero temperature and arbitrary magnetic field h by the bethe ansatz we present analytical results for the leading terms when h where is a known scale and a numerical solution for the entire range of fields in the second part we calculate susceptibility profiles near the boundary at finite temperature t numerically by using the density matrix renormalization group for transfer matrices and analytically for t 1 by field theoretical methods finally we compare b at finite temperature with a low temperature asymptotics which we obtain by combining our bethe ansatz result with recent predictions from bosonization

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

fluctuations of extensive functions of quenched random couplings an extensive quantity is a family of functions v of random parameters indexed by the finite regionsv subsets of d over which v are additive up to corrections satisfying the boundary estimate stated below it is shown that unless the randomness is nonessential in the sense that lim v v has a unique value in the absolute i e not just probabilistic sense the variance of such a quantity grows as the volume ofv of particular interest is the free energy of a system with random couplings for such v bounds are derived also for the generating functione et in a separate application variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment

new results for the xx model with boundaries in this paper we study the xx model with particular non diagonal boundaries using a fermionization technique for an extended version of this chain we are able to present a new operator which commutes with the extended and also the original hamiltonian it is a highly non trivial conserved quantity in the spin chain formalism which gives rise to an interesting combinatorial partition function

mixed hitting time models we study mixed hitting time models that specify durations as the first time a levy process a continuous time process with stationary and independent increments crosses a heterogeneous threshold such models are of substantial interest because they can be deduced from optimal stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards structure we show how strategies for analyzing the identifiability of the mixed proportional hazards model can be adapted to prove identifiability of a hitting time model with observed covariates and unobserved heterogeneity we discuss inference from censored data and give examples of structural applications we conclude by discussing the relative merits of both models as complementary frameworks for econometric duration analysis

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

non abelian gauge theory for quantum heisenberg antiferromagnetic chain a continuum su 2s u 1 gauge theory for a heisenberg antiferromagnet with arbitrary spin s is obtained we show that the level 1 su 2 wzw model with a certain marginally irrelevant perturbation describes the low energy phenomena of the heisenberg model with spin 1 2 the model with spins other than 1 2 can be described in the level 2s su 2 wzw model with a certain relevant perturbation we give a qualitative explanation of the haldane conjecture for heisenberg antiferromagnets

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

singular monge ampere foliations this paper generalizes results of lempert and szoke on the structure of the singular set of a solution of the homogeneous monge ampere equation on a stein manifold their a priori assumption that the singular set has maximum dimension is shown to be a consequence of regularity of the solution in addition their requirement that the square of the solution be c 3 everywhere is replaced by a smoothness condition on the blowup of the singular set under these conditions the singular set is shown to inherit a finsler metric which in the real analytic case uniquely determines the solution of the monge ampere equation these results are proved using techniques from contact geometry

the operator content of the exactly integrable su n magnets the operator content of the exactly integrable models associated with the su n lie algebras with periodic boundaries are studied the authors results were obtained from a numerical and analytical analysis of the associated bethe ansatz equations the resulting spectra indicate that the ferromagnetic and antiferromagnetic models have different operator content for n 2 being realizations of distinct modular invariant solutions

operator dimensions and surface exponents for the non linear schrodinger model at t 0 using the euler maclaurin formula the authors compute finite size corrections to the ground and excited state energies and momenta this enables them to obtain all possible operator scaling dimensions at the critical point t 0 and surface exponents for a variety of boundary conditions they extend the predictions of conformal invariance to include green functions with oscillating terms

conformal theory of spin correlations in the semi infinite 3 state potts and self dual zn models in the conformal theory the magnetization operator of the critical 3 state potts or self dual z3 model is degenerate at level 6 solving a sixth order differential equation the authors calculate the bulk 4 spin correlation function and the spin spin correlation function in the half space the spin spin correlation function of the semi infinite self dual zn model is also obtained for arbitrary n both free and fixed spin boundary conditions are considered

relaxation to equilibrium for two dimensional disordered ising systems in the griffiths phase we consider glauber type dynamics for two dimensional disordered magnets of ising type we prove that if the disorder averaged influence of the boundary condition is sufficiently small in the equilibrium system then the corresponding glauber dynamics is ergodic with probability one and the disorder average c t of time autocorrelation function satisfies for large t for the standard two dimensional dilute ising ferromagnet with i i d random nearest neighbor couplings taking the values 0 or j 0 0 our results apply even if the active bonds percolate and j 0 is larger than the critical value j c of the corresponding pure ising model for the same model we also prove that in the whole griffiths phase the previous upper bound is optimal this implies the existence of a dynamical phase transition which occurs when j crosses j c

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

the effect of attractive monomer monomer interactions on adsorption of a polymer chain the authors have used transfer matrix techniques to study a model of polymer adsorption and collapse they consider the conventional model of a self avoiding walk with attractive nearest neighbour interactions on the square lattice and introduce adsorbing boundaries the numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order there is also clear evidence that the collapse transition lowers the adsorption temperature estimates of the surface scaling dimensions at the ordinary theta transition support the conjecture of seno and stella 1988 that the surface critical behaviour at the theta and theta points belong to different universality classes

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

bethe ansatz results for hubbard chains with toroidal boundary conditions we solve exactly the problem of a one dimensional repulsive u hubbard chain with toroidal boundary conditions htb using the bethe ansatz approach we calculate analytically the finite size corrections to the ground state energy in the half filled case and use this expression to derive charge and spin stiffnesses with no assumptions we then use a particle hole transformation to calculate the finite size corrections for the half filledattractive u case and again derive the resulting expressions for the charge and spin stiffnesses lastly we discuss how the repulsive u corrections relate to those of a heisenberg model with toroidal boundary conditions

finite size effects and infrared asymptotics of the correlation functions in two dimensions the finite size corrections approach to the calculation of the asymptotics of correlation functions containing the oscillating terms in the asymptotics in 1 1 dimensional theories is presented explicit formulae for the critical exponents in integrable models are obtained

cost distributions in large combinatorial optimisation problems the authors have examined the cost distribution of locally optimal solutions in certain combinatorial optimisation problems this distribution is found to be peaked about a value characteristics of the algorithm involved with a width that decreases with the system size n it is shown that the distribution of costs epsilon is of the form exp ng epsilon and that g epsilon is self averaging consequently estimation of the optimal cost is best achieved by curve fitting to g epsilon possible forms for g epsilon are proposed

discontinuity of the percolation density in one dimensional 1 x y 2 percolation models we consider one dimensional percolation models for which the occupation probability of a bond kx y has a slow power decay as a function of the bond s length for independent models and with suitable reformulations also for more general classes of models it is shown that i no percolation is possible if for short bondskx y p 1 this dichotomy resembles one for the magnetization in 1 x y 2 ising models which was first proposed by thouless and further supported by the renormalization group flow equations of anderson yuval and hamann the proofs of the above percolation phenomena involve rigorous renormalization type arguments of a different sort

marginal extended perturbations in two dimensions and gap exponent relations the most general form of a marginal extended perturbation in a two dimensional system is deduced from scaling considerations it includes as particular cases extended perturbations decaying either from a surface a line or a point for which exact results have been previously obtained the first order corrections to the local exponents which are functions of the amplitude of the defect are deduced from a perturbation expansion of the two point correlation functions assuming covariance under conformal transformation the perturbed system is mapped onto a cylinder working in the hamiltonian limit the first order corrections to the lowest gaps are calculated for the ising model the results confirm the validity of the gap exponent relations for the perturbed system

a test for normality based on the empirical characteristic function summary an omnibus test of normality is proposed which has high power against many alternative hypotheses the test uses a weighted integral of the squared modulus of the difference between the characteristic functions of the sample and of the normal distribution together with the one to one correspondence between t and f x suggest utilizing kn t in statistical inference here we use n t to test the composite hypothesis that f x is normal let 00 t exp it1 1t2 a2 be the characteristic function under the null hypothesis with 1u and u2 the unspecified mean and variance the test introduced here is based on a weighted integral over t of the squared modulus of kn t o t where 0 t depends on sample estimates of ju and a2 we compare the power of the test with that of prominent tests based on order statistics and on sample moments heathcote 1972 and feigin heathcote 1977 have previously considered using either the real or imaginary part alone of 4n t in tests of simple hypotheses their tests relied on the fact that for given t either component of 4n t is asymptotically normal with mean given by its population counterpart if the alternative hypothesis is also simple it may be possible to find a value of t that maximizes the power of the test in large samples epps singleton pulley 1982 showed how the sample moment generating function may be employed to test composite hypotheses that the data come from one or the other of two separate families of distributions murota takeuchi 1981 have recently proposed a location and scale invariant test based on the statistic an t i n t s 12 where s is the sample standard deviation applied to the problem of testing normality an t was found to have high power in the vicinity of t 10 against members of six families of symmetric alternatives but its

the lowest excitations in the spin s xxx magnet and conformal invariance the bethe ansatz equations for the integrable spin s isotropic heisenberg antiferromagnet are solved numerically at a finite number of sites n the vacuum and the lowest singlet and triplet solutions are presented for s 1 2 2 up to sn 240 through extrapolation of the finite size data the central charge and anomalous dimensions of the scaling operators for the underlying conformal field theory are calculated and found to agree with the expected theoretical values the status of the bethe string hypothesis about the structure of the solutions is discussed based on the obtained computer data up to s 9 2

characterization of strictly convex domains biholomorphic to a circular domain recently parabolic exhaustions have been used successfully to classify complex spaces stoll 6 and 7 burns 2 p wong 9 here we define parabolic exhaustions for strictly convex domains in c and give necessary and sufficient conditions for such a domain to be biholomorphically equivalent to a circular domain or even to the ball the results presented in this note are part of the ph d thesis the author is completing under the direction of professor w stoll details and more implications will appear at a later date a strictly convex domain d c c is a domain for which there exists a defining function whose real hessian is strictly positive on tx dd for all x g dd let a be the open unit disk in c and let s be the unit sphere in c let d c c be a strictly convex domain and p e d be any point for b g s lempert 4 constructs an extremal map f d b a d which is holomorphic with f 0 6 v and f 0 6 x where 1 x 0 is the length of b in the infinitesimal kobayashi metric of d at p these conditions determine f d b uniquely and the map extends smoothly to an embedding f u b s d also f a x s d is of class c and surjective one and only one function r d r exists such that r f z b z for z b g a x s then r is a continuous exhaustion of d positive and of class c on d p also r 1 on 3d we refer to r as the lempert exhaustion of d at p

an improved version of the quandt ramsey mgf estimator for mixtures of normal distributions and switching regressions quandt and ramsey have suggested an estimator for normal mixtures and switching regressions which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function this paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares when this is done more points of evaluation moments are unambiguously better than less most of the results presented are also applicable to method of moments estimators in general

some exact results for moments of 2d directed animals using computer enumerations and the algebraic approximant method of series analysis several new exact results have been found for moments of width perimeter and loops for directed animals on the square and triangular lattices a proof using q series is given for exact solutions for widths on both the square and triangular lattices

gauge symmetries and percolation in j ising spin glasses we consider the j spin glass on a finite graph g v e with i i d couplings our approach considers the z2 local gauge invariance of the system we see the gauge group as a graph theoretic linear code over gf 2 the gauge is fixed by choosing a convenient linear supplement of assuming some relation between the disorder parameter p and the inverse temperature of the thermal bath pb we study percolation in the random interaction random cluster model and extend the results to dilute spin glasses

exact theory of polymer adsorption in analogy with the kondo problem we conjecture the exact scaling theory for the adsorption of two dimensional polymers by using boundary s matrices we compute the boundary free energy the g function study the flow from the adsorbed to the desorbed phase and derive the crossover exponent and all the geometrical exponents at the transition more generally we solve the special transition in the o n model the polymer case corresponding to n 0 the n 2 limit appears identical to the ordinary kondo problem

a general euclidean connection for the so n m lie algebra and the algebraic approach to scattering we obtain a general euclidean connection for the so n m lie algebra this euclidean connection allows an algebraic derivation of the s matrix and it reduces to the known connection in suitable circumstances

integrable spin 1 2 xxz heisenberg chain with competing interactions the critical behaviour of an integrable model of a spin 1 2 chain with nearest neighbour xxz interaction and a competing three spin interaction involving nearest and next nearest neighbours is studied the phase diagram at zero temperature is obtained methods from conformal field theory are used to compute the asymptotics of the spin spin correlation functions

transform estimation of parameters for stage frequency data we consider multistage development models that occur in the maturation of biological organisms disease progressions and industrial processes the situations that we address are distinguished by the essentially destructive sampling required to assess the stage reached by each individual we develop robust estimators of stage dependent maturation rates and overall death rates using method of moments based on laplace transforms for which we develop variance estimates under different sampling schemes we apply these methods to studies of cattle parasite and grasshopper life cycles and show that the laplace methods compare well with maximum likelihood methods

on the swendsen wang dynamics i exponential convergence to equilibrium we present rigorous results on the exponential convergence to equilibrium for the swendsen wang stochastic dynamics for thed dimensional ising ferromagnet with external magnetic fieldh in the thermodynamic limit we consider various situations mainly in the low temperature regime in which boundary conditions are homogeneous and parallel or opposite to the external field in the latter case we relate directly the tunneling from the metastable phase to the stable one with the exponential convergence to equilibrium

relaxation of disordered magnets in the griffiths regime we study the relaxation to equilibrium of discrete spin systems with random finite range not necessarily ferromagnetic interactions in the griffiths regime we prove that the speed of convergence to the unique reversible gibbs measure is almost surely faster than any stretched exponential at least if the probability distribution of the interaction decays faster than exponential e g gaussian furthermore if the interac tion is uniformly bounded the average over the disorder of the time autocorrelation function goes to equilibrium as exp k log t d d 1 in d 1 in agreement with previous results obtained for the dilute ising model

some finite size amplitudes and critical exponents for potts and ashkin teller quantum chains analytic expressions are derived for the leading finite size corrections to a class of energy eigenvalues of the potts and ashkin teller quantum chains making use of their equivalences with a modified xxz heisenberg chain assuming conformal invariance exact results are thence obtained for some bulk scaling dimensions and surface exponents in these models

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

the number of metastable states in the projection rule neural network we calculate the direct average n of the number of metastable states in the projection rule neural network by means of the saddle point method n is obtained as a function of the hamming distance g to a given pattern stability gamma and energy e the critical storage capacity of the model is calculated the examination of the energy dependence of n leads to lower bounds for the energies of the spin glass states

the asymptotic expansion of a cr invariant and grauert tubes cr manifolds the abstract models of real hypersurfaces in complex manifolds are 2n 1 dimensional manifolds m with a codimension one subbundle h of the tangent bundle which carries a complex structure the cr refers to cauchy riemann because for m c c n l the subbundle h consists of induced cauchy riemann operators there is a wealth of geometry and analysis associated with these structures especially when the cr manifolds are strictly pseudoconvex for example two strictly pseudoconvex domains are biholomorphically equivalent if and only if their boundaries are cr equivalent a fundamental problem in cr geometry is to find computable invariants associated with the cr structures the global cr invariant we will consider in this paper is the chem simons type invariant discovered by bums and epstein b e 1 it is a real valued global cr invariant of a compact 3dimensional strictly pseudo convex cr manifold whose holomorphic tangent bundle is trivial cheng and lee independently found this invariant and extend the definition of b e invariant to a relative invariant on an arbitrary compact 3 dimensional cr manifold cf c l we will evaluate this g asymptotically on the boundary of small grauert tubes before posing the question in a more precise form we will first say a few workds about grauert tubes let x be a real analytic manifold then every coordinate patch u c r n can be thickened to obtain an open set r c c n since the coordinate changes of x are real analytic maps by taking power series expansions and by shrinking c u to get convergence they can be extended holomorphically to such enlarged domains and thus they can be used as holomorphic transition

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

the one dimensional hubbard model with open ends universal divergent contributions to the magnetic susceptibility the magnetic susceptibility of the one dimensional hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields including leading and next leading orders logarithmic contributions to the bulk part are identified as well as algebraic logarithmic divergences in the boundary contribution as a manifestation of spin charge separation the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the heisenberg model for the bulk part at zero temperature the scale in the logarithms is determined exactly from the bethe ansatz at finite temperature the susceptibility profile as well as the friedel oscillations in the magnetization are obtained numerically from the density matrix renormalization group applied to transfer matrices agreement is found with an exact asymptotic expansion of the relevant correlation function

excited states in the twisted xxz spin chain we compute the finite size spectrum for the spin chain with twisted boundary conditions for anisotropy in the regime and arbitrary twist the string hypothesis is employed for treating complex excitations the bethe ansatz equtions are solved within a coupled nonlinear integral equation approach with one equation for each type of string the root of unity quantum group invariant periodic chain reduces to the chain with a set of twist boundary conditions an integer multiple of for this model the restricted hilbert space corresponds to a unitary conformal field theory and we recover all primary states in the kac table in terms of states with specific twist and strings

complex monge ampere equations and totally real submanifolds abstract we study the dirichlet problem for complex monge ampere equations in hermitian manifolds with general non pseudoconvex boundary our main result theorem 1 1 extends the classical theorem of caffarelli kohn nirenberg and spruck in c n we also consider the equation on compact manifolds without boundary attempting to generalize yau s theorems in the kahler case as applications of the main result we study some connections between the homogeneous complex monge ampere hcma equation and totally real submanifolds and a special dirichlet problem for the hcma equation related to donaldson s conjecture on geodesics in the space of kahler metrics

inhomogeneous percolation problems and incipient infinite clusters the authors consider inhomogeneous percolation models with density pc f x and examine the forms of f x which produce incipient structures taking f x approximately mod x mod lambda and assuming the existence of a correlation length exponent v for the homogeneous percolation model they prove that in d 2 the borderline value of lambda is lambda b 1 v if lambda 1 v then with probability one there is no infinite cluster while if lambda 2 the models studied suggest what sort of incipient objects should be examined in random surface models

off diagonal density profiles and conformal invariance off diagonal profiles of local densities e g order parameter or energy density are calculated at the bulk critical point by conformal methods on a strip with transverse coordinate v for different types of boundary conditions free fixed and mixed such profiles which are defined by the non vanishing matrix element of the appropriate operator between the ground state and the corresponding lowest excited state of the strip hamiltonian enter into the expression of two point correlation functions on a strip they are of interest in the finite size scaling study of bulk and surface critical behaviour since they allow the elimination of regular contributions the conformal profiles which are obtained through a conformal transformation of the correlation functions from the half plane to the strip are in agreement with the results of a direct calculation for the energy density of the two dimensional ising model

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

another critical exponent inequality for percolation β 2 δ the inequality in the title is derived for standard site percolation in any dimension assuming only that the percolation density vanishes at the critical point the proof based on a lattice animal expansion is fairly simple and is applicable to rather general site or bond short or long range independent percolation models

finite size effects in a non half filled hubbard chain the finite size effects in the spectrum of a hubbard chain are obtained for both the repulsive and attractive cases it is shown that the finite size corrections similar to the case of a heisenberg chain or bose gas are nonanalytic unless some conditions are imposed on the chemical potential magnetic field and chain length if these conditions are met the spectrum shows a similar tower structure as expected in conformal theories although the model in general is not conformally invariant in the special case when the two fermi velocities are equal the model is conformally invariant with c 2 the indices are similar to the gaussian form and there are four marginal operators

percolation phenomena in low and high density systems we consider the 2d quenched disordered q state potts ferromagnets and show that in the translation invariant measure averaged over the disorder at self dual points any amalgamation of q 1 species will fail to percolate despite an overall high density of 1 q 1 further in the dilute bond version of these systems if the system is just above threshold then throughout the low temperature phase there is percolation of a single species despite a correspondingly small density finally we demonstrate both phenomena in a single model by considering a perturbation of the dilute model that has a self dual point we also demonstrate that these phenomena occur by a similar mechanism in a simple coloring model invented by o haggstrom

new solutions of the bethe ansatz equations for the isotropic and anisotropic spin 1 2 heisenberg chain bethe ansatz equations bae are investigated for the isotropic spin 1 2 heisenberg chain as well as the xxz chain with real solutions characterized by identical integers in the logarithmic form of the bae such states do not belong to the usual classification scheme string hypothesis they always exist in critical sectors with respect to the total spin of the chain and the anisotropy the conception of holes has to be changed in this case because there occur more holes than expected the finite size corrections for the xxx model are calculated including complex roots and the new type of real solutions with repeating integers the tower structure predicted by the hypothesis of conformal invariance is shown to remain unchanged

surface free energy for systems with integrable boundary conditions the surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions we use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators specializing to the xxz spin 1 2 chain we introduce a novel finite temperature boundary operator which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions

conformal invariance and critical exponents of the takhtajan babujian models the authors are concerned with the critical properties of antiferromagnetic takhtajan babujian models with spin s 1 3 2 and 2 the leading eigenenergies of this hamiltonian in a finite chain are calculated by investigating numerically and analytically the bethe ansatz equations for the finite system the critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite hamiltonian the appearance of logarithmic corrections produces poor estimates however a combination of analytical and numerical methods produces very good estimates their results strongly support the conjecture that the wess zumino witten novikov non linear sigma models with topological charge k 2s are the underlying field theories for these spin s statistical mechanics models

string like lattice models and hecke algebras the author discusses lattice statistical mechanical models with n dimensional static endpoint string like degrees of freedom in the infinite string tension limit these models give representations of hecke algebras hk q quotient algebras of which may be used to construct virasoro algebras in the limit k to infinity and when q 4 cos2 pi r r epsilon z they give the regular representation and well defined representations associated with and containing each irreducible representation including non unitarisable cases they use these models to obtain a complete set of primitive idempotents and hence the central idempotents of the generic algebra

empirical transform estimation for indexed stochastic models we present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms asymptotic approximations are derived for the distribution of the resulting estimators an explicit expression for the mean squared error provides a natural way of selecting the transform variable and a numerical example illustrates the performance of the resulting method a common finding which we term diagonal optimization occurs when multiparameter models are fitted by using transforms diagonal optimization arises when optimal performance results from equating the elements of the transform vector and we provide a heuristic explanation of why this occurs

interfaces in the potts model i pirogov sinai theory of the fortuin kasteleyn representation we develop a new analysis of the order disorder transition in ferromagnetic potts models for large numberq of spin states we use the pirogov sinai theory which we adapt to the fortuin kasteleyn representation of the models this theory applies in a rather direct way in our approach and leads to a system of non interacting contours with small activities as a consequence simpler and more natural techniques are found allowing us to recover previous results on the bulk properties of the model which then extend to non integer values ofq and to deal with non translation invariant boundary conditions this will be applied in a second part of this work to study the behaviour of the interfaces at the transition point

finite size corrections for spin s heisenberg chains and conformal properties the author compares recent results on finite size corrections for the isotropic xxx heisenberg chain and its integrable generalisations with former numerical and analytic calculations for the ground state and its lowest excitations leading and non leading terms are considered the analysis confirms the predictions of conformal invariance and sheds some new light on the fine structure of finite size corrections

convergence to equilibrium of random ising models in the griffiths phase we consider glauber type dynamics for disordered ising spin systems with nearest neighbor pair interactions in the griffiths phase we prove that in a nontrivial portion of the griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1 this condition has in turn been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential and that the average over the disorder of the time autocorrelation function goes to equilibrium faster than exp k log t d d 1 we then show that for the diluted ising model these upper bounds are optimal

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

estimation of stage duration distributions and mortality under repeated cohort censuses many processes in nature can be viewed as arising from subjects progressing through sequential stages and may be described by multistage models examples include disease development and the physiological development of plants and animals we develop a multistage model for sampling designs where a small set of subjects is followed and the number of subjects in each stage is assessed repeatedly for a sequence of time points but for which the subjects cannot be identified the motivating problem is the laboratory study of developing arthropods through stage frequency data our model assumes that the same individuals are censused at each time introducing among sample dependencies this type of data often occur in laboratory studies of small arthropods but their detailed analysis has received little attention the likelihood of the model is derived from a stochastic model of the development and mortality of the individuals in the cohort we present an mcmc scheme targeting the posterior distribution of the times of development and times of death of individuals this is a novel type of mcmc that uses customized proposals to explore a posterior with disconnected support arising from the fact that individual identities are unknown the mcmc algorithm may be used for inference about parameters governing stage duration distributions and mortality rates the method is demonstrated by fitting the development model to stage frequency data of a mealybug cohort placed on a grape vine

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

boundary conditions and the free energy for statistical mechanical models the author shows that the choice of boundary conditions can significantly affect the calculation of the free energy for discrete statistical mechanical models on finite or semi infinite lattices when the exponentiated coupling is extended into the complex plane he shows however that the boundary conditions most consistent with boundary configuration independence in the direction in which a lattice is infinite give a unique analytic function for the free energy this unique function is the free energy most appropriate for extrapolation to the full thermodynamic limit the author shows that such boundary conditions are orthogonal to all but one degenerate ferromagnetic ground states at zero temperature

correlation length bounds for disordered ising ferromagnets thed dimensional nearest neighbor disordered ising ferromagnet h sum j ij sigma i sigma j is studied as a function of both temperature t and a disorder parameter which measures the size of fluctuations of couplingsjij 0 a finite size scaling correlation length f t is defined in terms of the magnetic response of finite samples this correlation length is shown to be equivalent in the scaling sense to the quenched average correlation length t defined as the asymptotic decay rate of the quenched average two point function furthermore the magnetic response criterion which defines f is shown to have a scale invariant property at the critical point the above results enable us to prove that the quenched correlation length satisfies c left log xi t right xi t geqq left t t c right 2 mathord left vphantom 2 d right kern nulldelimiterspace d which implies the boundv 2 d for the quenched correlation length exponent

intertwining vectors and the connection between critical vertex and sos models a new algebraic bethe ansatz construction for the six vertex model is formulated using intertwining vectors and local gauge transformations a new set of eigenvectors and their associated eigenvalue equations are derived this basis is well suited to connect vertex sos and rsos models exact relations on a finite lattice between vertex and sos models are proven with the help of the intertwining vectors

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

calculation of finite size corrections for the antiferromagnetic heisenberg chain the finite size corrections for the anisotropic heisenberg model in the gap region are calculated using an exact integral representation based on the bethe ansatz equations bae the energy corrections are determined by saddle point approximations for states without complex roots the case of symmetric states is discussed in greater detail

conformal invariance studies of the baxter wu model and a related site colouring problem the partition function of the baxter wu model is exactly related to the generating function of a site colouring problem on a hexagonal lattice we extend the original bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions the operator content of these models is studied by solving numerically the bethe ansatz equations and by exploring conformal invariance since the eigenspectra are calculated for large lattices the corrections to finite size scaling are also calculated

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea