Cluster Variation Method, Pade` Approximants and Critical Behaviour

TL;DR

This paper demonstrates a simple method using Padé approximants applied to cluster variation method results to accurately estimate critical exponents in the Ising model and surface critical phenomena.

Contribution

It introduces a straightforward approach to extract non-classical critical exponents from mean field-like approximations using Padé analysis, validated across various lattice types.

Findings

Accurate critical exponents obtained for different lattices.

Good agreement with exact and numerical results.

Method effective for surface critical behavior analysis.

Abstract

In the present paper we show how non--classical, quite accurate, critical exponents can be extracted in a very simple way from the Pad\'e analysis of the results obtained by mean field like approximation schemes, and in particular by the cluster variation method. We study the critical behavior of the Ising model on several lattices (quadratic, triangular, simple cubic and face centered cubic) and two problems of surface critical behaviour. Both unbiased and biased approximants are used, and results are in very good agreement with the exact or numerical ones.