Cluster variation method and disorder varieties of two-dimensional Ising-like models

Abstract

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 nearest-neighbor, next-nearest-neighbor and plaquette interactions, and, after rederiving known results, report simple closed-form expressions for the pair and plaquette correlation functions.

10 revtex pages, 1 postscript figure

References in corpus (1)

• Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models

Cited by in corpus (5)

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• Pair correlations and structure factor of the $J_1$-$J_2$ square lattice Ising model in an external field within the Cluster Variation Method
• Disorder solutions for the free energy of the Ising-like models