upper bounds on the critical temperature for various ising models upper bounds are obtained for spin 1 systems in the case of only nearestneighbor interactions on for example the square lattice we obtain cj 0 3592 the method s strength is seen when considering systems with longer range interactions for example we obtain cj 0 360 compared to the previous best bound of c j 0 345 for the one dimensional lattice with 1 r2 interactions the method relies upon an identity between correlation functions and then the use of correlation inequalities to obtain the final bounds

comparison of three correlation coefficient estimators for gaussian stationary processes using independent samples from two stationary gaussian processes second order statistics are examined for the following three correlation estimators 1 the direct estimator 2 a hybrid sign estimator and 3 the polarity coincidence estimator in most cases increasing the number of samples by a factor of two or three allows one to use the simple polarity coincidence estimator with the same accuracy as the other two estimators

a generalized discrepancy and quadrature error bound an error bound for multidimensional quadrature is derived that includes the koksma hlawka inequality as a special case this error bound takes the form of a product of two terms one term which depends only on the integrand is defined as a generalized variation the other term which depends only on the quadrature rule is defined as a generalized discrepancy the generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the l p star discrepancy and p that arises in the study of lattice rules

an intermediate phase with slow decay of correlations in one dimensional 1 x y 2 percolation ising and potts models we rigorously establish the existence of an intermediate ordered phase in one dimensional 1 x y 2 percolation ising and potts models the ising model truncated two point function has a power law decay exponent which ranges from its low and high temperature value of two down to zero as the inverse temperature and nearest neighbor coupling vary similar results are obtained for percolation and potts models

tri critical behavior of the blume emery griffiths model on a kagome lattice effective field theory and rigorous bounds abstract spin correlation identities for the blume emery griffiths model on kagome lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature from the spin correlation identities the mean field approximation and the effective field approximation results for the magnetization the critical frontiers and the tricritical points are obtained the rigorous upper bounds on the critical temperature improve over those effective field type theories results

efficient methods of estimate correlation functions of gaussian processes and their performance analysis new efficient methods to estimate crosscorrelation functions of gaussian signals are studied in these methods the covariance property of the gaussian distribution is utilized such that the correlation estimates can be computed with only additions to evaluate the performances of the methods exact expressions for the bias and variance of these estimators are formulated and utilized in comparing these methods with the conventional correlation estimator as a result we point out that these new methods can give estimates which are comparable to the conventional approach

correlations equalities and some upper bounds for the critical temperature for spin one systems abstract starting from correlation identities for the blume capel spin 1 systems and using correlation inequalities we obtain rigorous upper bounds for the critical temperature the obtained results improve over effective field type results

upper bound on the critical temperature in the 3d ising model the upper bound on the critical temperature in the ising model recently derived from callen s correlation equalities by sa barreto and o carroll 1983 and improved by monroe 1984 is further improved by a more economical use of messager and miracle sole inequalities starting from a different callen correlation equality

markov processes as a tool in field theory abstract in a recent paper brydges frohlich and spencer have successfully applied markov chains to classical spin systems using probabilistic methods in a more systematic way we improve some of their results the methods can be extended to fields with continuous parameter such as p fields

correlation estimators based on simple nonlinear transformations the computational cost of estimating correlations may be reduced by employing sums of simple nonlinear functions of the data a quadruplex transformation is presented and the performance of the associated estimator is analyzed for real and complex gaussian processes with independent observations the variance of the estimator is approximately 14 higher than that obtained by averaging lag products

a phase cell cluster expansion for a hierarchical o 3 4 model the formalism developed in a previous paper is applied to yield a phase cell cluster expansion for a hierarchical b model the field is expanded into modes with specific renormatization group scaling properties the present cluster expansion for a vacuum expectation value is formally the natural factorization of each term in the perturbation expansion into the contribution of modes connected to the variables in the expectation via interactions and that of the complementary set the expectation value is thus realized as a sum of contributions due to finite subsets of the modes we emphasize the following additional features 1 partitions of unity are not used 2 there are essentially no cut offs 3 the expansion is developed directly without an initial need to prove an ultraviolet stability bound the most difficult part of the traditional approach our main interest in the present phase cell cluster expansion is founded in the belief that it may be the right vehicle for proving the existence of a non trivial four dimensional field theory

mean field bounds and correlation inequalities i prove a new correlation inequality for a class ofn component classical ferromagnets 1 n 4 this inequality implies that the correlation functions decay exponentially and the spontaneous magnetization is zero above the mean field critical temperature

on a fast digital method of estimating the autocorrelation of a gaussian stationary process the zero mean stationary gaussian processes have the property that if they are input into an instantaneous nonlinear device the cross correlation of input and output is proportional to the auto correlation of the input this suggests an estimation procedure for the autocorrelation function based mainly on additions which is a modified type of the pcc polarity coincidence correlator the object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties as a reference some examples are provided which compare the behavior of the modified ppc estimator to the classical one based on products and additions

low discrepancy sequences in high dimensions how well are their projections distributed quasi monte carlo qmc methods have been successfully used to compute high dimensional integrals arising in many applications especially in finance to understand the success and the potential limitation of qmc this paper focuses on quality measures of point sets in high dimensions we introduce the email protected superposition and truncation discrepancies which measure the quality of selected projections of a point set on lower dimensional spaces these measures are more informative than the classical ones we study their relationships with the integration errors and study the tractability issues we present efficient algorithms to compute these discrepancies and perform computational investigations to compare the performance of the sobol nets with that of the sets of latin hypercube sampling and random points numerical results show that in high dimensions the superiority of the sobol nets mainly derives from the one dimensional projections and the projections associated with the earlier dimensions for order 2 and higher order projections all these point sets have similar behavior on the average in weighted cases with fast decaying weights the sobol nets have a better performance than the other two point sets the investigation enables us to better understand the properties of qmc and throws new light on when and why qmc can have a better or no better performance than monte carlo for multivariate integration in high dimensions

efficient autocorrelation estimation using relative magnitudes the relative magnitude estimator computes the normalized autocorrelation of a stationary gaussian process using simple nonlinear functions to eliminate most multiplications approximate expressions for bias and variance of the estimate are presented along with the results of a computer simulation the estimator performs well when compared to similar techniques

correlation identities and rigorous upper bounds on the critical temperature for the spin 1 blume capel model on a kagome lattice abstract spin correlation identities for the blume capel model on kagome lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature from the spin correlation identities the mean field approximation and the effective field approximation results for the magnetization the critical frontiers and the tricritical points are obtained the rigorous upper bounds on the critical temperature improve over those effective type theories results

a new randomized algorithm to approximate the star discrepancy based on threshold accepting we present a new algorithm for estimating the star discrepancy of arbitrary point sets similar to the algorithm for discrepancy approximation of winker and fang siam j numer anal 34 1997 pp 2028 2042 it is based on the optimization algorithm threshold accepting our improvements include amongst others a nonuniform sampling strategy which is more suited for higher dimensional inputs and additionally takes into account the topological characteristics of given point sets and rounding steps which transform axis parallel boxes on which the discrepancy is to be tested into critical test boxes these critical test boxes provably yield higher discrepancy values and contain the box that exhibits the maximum value of the local discrepancy we provide comprehensive experiments to test the new algorithm our randomized algorithm computes the exact discrepancy frequently in all cases where this can be checked i e where the exact discrepancy of the point set can be computed in feasible time most importantly in higher dimensions the new method behaves clearly better than all previously known methods

higgs 2 3 quantum fields in a finite volume we consider a euclidean model of interacting scalar and vector fields in two and three dimensions and prove a lower bound for vacuum energy in a lattice approximation the bound is independent of a lattice spacing it is proved with the help of renormalization transformations in wilson kadanoff form it extends in principal also to generating functional for schwinger functions

average case complexity of multivariate integration we study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical wiener sheet measure to derive the average case complexity one needs to obtain optimal sample points we prove that optimal design is closely related to discrepancy theory which has been extensively studied for many years this relation enables us to show that optimal sample points can be derived from hammersley points extending the result of roth and using the recent result of wasilkowski we conclude that the average case complexity is e 1 lne 1 d 1 2

an efficient technique for high correlation estimation two sum based estimators are proposed as fast accurate methods for estimating the normalized acf of stationary processes for gaussian processes their performances are evaluated in terms of bias and covariance and are compared to the ones of the conventional direct estimator and of the hybrid sign and the polarity coincidence fast methods for high correlation values the proposed estimators exhibit the same accuracy as the direct estimator

a note on the computational complexity of high correlation estimators two fast estimators of correlation coefficients namely the absolute difference average ada and the relative magnitude rm correlators have been proposed as well suited for high correlation estimation it is shown that equivalent implementations of the ada estimators actually require the same number of additions and comparisons as the rm estimator the computational costs of the two estimators are the same

good permutations for deterministic scrambled halton sequences in terms of l2 discrepancy one of the best known low discrepancy sequences used by many practitioners is the halton sequence unfortunately there seems to exist quite some correlation between the points from the higher dimensions a possible solution to this problem is the so called scrambling in this paper we give an overview of known scrambling methods and we propose a new way of scrambling which gives good results compared to the others in terms of l 2 discrepancy on top of that our new scrambling method is very easy to implement

uniform design theory and application a uniform design ud seeks design points that are uniformly scattered on the domain it has been popular since 1980 a survey of ud is given in the first portion the fundamental idea and construction method are presented and discussed and examples are given for illustration it is shown that ud s have many desirable properties for a wide variety of applications furthermore we use the global optimization algorithm threshold accepting to generate ud s with low discrepancy the relationship between uniformity and orthogonality is investigated it turns out that most ud s obtained here are indeed orthogonal

the blume emery griffiths model at an infinitely many ground states interface and exponential decay of correlations at all non zero temperatures in this paper we study the spin spin correlation function decay properties of the blume emery griffiths beg model with hamiltonian located on the interface between the disordered and the anti quadrupolar phases on this interface the beg model has infinitely many ground state configurations we show that for any dimension d there exists a parameter value yd below which the spin spin correlation function with zero boundary condition decays exponentially fast at all non zero temperatures this result suggests that reentrant behaviour predicted by mean field and numerical calculations may be absent for those values of parameters

upper bounds on the critical temperature for the two dimensional blume emery griffiths model we obtain rigorous upper bounds for the critical temperature associated with second order phase transitions of the two dimensional spin 1 beg model for real values ofk andd coupling constants and forj 0 we use some correlation equalities and inequalities to show the exponential decay of the two point function characterizing the disordered phase

critical point dominance in one dimension the renormalized dimensionless 4 point coupling constant of scalar one dimensional field theories is maximized uniquely by the critical point theories obtainable as the scaling limit of 4 models the renormalized coupling constant of certain scalar one dimensional lattice field theories is maximized uniquely for fixed correlation length by the corresponding spin 1 2 model

asymptotic properties of the spectral test diaphony and related quantities this paper presents the limit laws of discrepancies defined via exponential sums and algorithms with error bounds to approximate the corresponding distribution functions the results cover the weighted and the nonweighted spectral test of hellekalek and various instances of the general discrepancies of hiekernell and hoogland and kleiss for the exponential function system as well as classical quantities like the spectral test diaphony and the zaremba figure of merit

the random walk representation of classical spin systems and correlation inequalities ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion by using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities as an application of these inequalities we obtain a simple proof of the mass gap for the 4 2 quantum field model we also establish new upper bounds on critical temperatures

comment on ising models on hyperbolic graphs new proofs are given for propositions 1 and 2 of c c wu j stat phys 50 251 1996 the propositions involved upper and lower bounds on the critical temperature for these models besides being more direct than the previous proofs the new proofs improve both bounds

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

performances of the hybrid sign correlation coefficient estimator for gaussian stationary processes the hybrid sign estimator is a method of estimating the autocorrelation coefficient for gaussian stationary processes based on sums in this correspondence the features of such an estimator are examined both for uncorrelated pairs of samples and for correlated pairs with an assigned autocorrelation function of the process a generalized estimator is considered by varying the spacing between the pairs of samples the performances in terms of bias covariance and variance are given in simple approximate formulas and compared in comprehensive diagrams to the direct estimator based on sums of products and the polarity coincidence estimator based on counters

upper bounds on tc for classical ising models using correlation inequalities following closely the work of sa barreto and o carroll 1983 the author improves the upper bounds they derive for the critical temperature of classical ising ferromagnetics the improvement is achieved by a more critical use of griffith s 1967 inequalities at one point along with a completely new use of messager and miracle sole 177 inequalities at another stage of the proof

efficient algorithms for computing the l 2 discrepancy the l 2 discrepancy is a quantitative measure of precision for multivariate quadrature rules it can be computed explicitly previously known algorithms needed o m 2 operations where m is the number of nodes in this paper we present algorithms which require o m log m d operations