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

TL;DR

This paper demonstrates that the cluster variation method provides exact results for disorder varieties in two-dimensional Ising-like models with competing interactions, exemplified through a square lattice model with multiple interactions.

Contribution

It shows that the cluster variation method yields exact results on disorder varieties in 2D Ising-like models with competing interactions, including explicit correlation functions.

Findings

Exact results for disorder varieties obtained via cluster variation method

Closed-form expressions for pair and plaquette correlation functions

Application to square lattice models with multiple interactions

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.