Journal of Physics A Mathematical and General

Variational approximations and mean-field scaling theory

Anastasios Malakis, S.S. Martinos

Published Nov 21, 1994• 1 citation

Abstract

It is shown that 'mean-field finite-size scaling theory' can be adjusted and applied to sequences of approximations that do not obey the well known power laws of finite-size scaling. The proposed modification of the theory seems to be well directed to the sequence of Baxter's variational approximations. This sequence of approximations shows a novel feature according to which exponential laws appear in places where power laws should be expected, but the modified scaling theory still yields relations from which non-classical critical exponents can be estimated. Thus, two techniques for the estimation of the critical exponent beta are suggested from the finite-order variational approximations. These techniques are applied to the zero-field Ising model on the square lattice using the systematic series of the Baxter-Tsang systems and excellent estimates of beta are obtained correct up to 13 significant figures.

DOI: 10.1088/0305-4470/27/22/007

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