Deriving exact results for Ising-like models from the cluster variation method
نویسنده
چکیده
The cluster variation method (CVM) is an approximation technique which generalizes the mean field approximation and has been widely applied in the last decades, mainly for finding accurate phase diagrams of Ising-like lattice models. Here we discuss in which cases the CVM can yield exact results, considering: (i) one-dimensional systems and strips (in which case the method reduces to the transfer matrix method), (ii) tree-like lattices and (iii) the so-called disorder points of euclidean lattice models with competitive interactions in more than one dimension.
منابع مشابه
Cluster variation method and disorder varieties of two–dimensional Ising–like models
I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into these models. I consider, as an example, the plaquette approximation of the cluster variation method for the square lattice Ising model with n...
متن کاملO ct 1 99 9 Cluster variation – Padé approximants method for the simple cubic Ising model
The cluster variation – Padé approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like models. Here the method is applied to the three-dimensional simple cubic Ising model, and new results, obtained with an 18-site basic cluster, are reported. O...
متن کاملCluster-variation-Pade-approximant method for the simple cubic Ising model
The cluster-variation-Pade-approximant method is a recently proposed tool, based on the extrapolation of low- and high-temperature results obtained with the cluster-variation method, for the determination of critical parameters in Ising-like models. Here the method is applied to the three-dimensional simple cubic Ising model, and new results, obtained with an 18-site basic cluster, are reported...
متن کاملCasimir interactions in Ising strips with boundary fields: exact results.
An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controlled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for...
متن کاملCluster Variation Method in Statistical Physics and Probabilistic Graphical Models
The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising–like) models in equilibrium statistical mechanics, improving on the mean–field approximation and the Bethe–Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problem...
متن کامل