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Nuclear Physics B - Proceedings Supplements

Deriving exact results for Ising-like models from the cluster variation method

Alessandro Pelizzola

Published Mar 1, 2000• 3 citations
Publisher
DOI
10.1016/s0920-5632(00)00457-6

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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.
The cluster variation method is a powerful hierarchy of mean-field-like approximations for Ising-like lattice models, which is known to give results that are particularly accurate at high and/or low temperature and converge to the exact ones as the size of the clusters taken into account gets larger. Here we show how these properties can be exploited to obtain non-classical, quite accurate estimates of quantities characterizing the critical behavior of the ordinary Ising model and the ground state of the triangular Ising antiferromagnet.