Application of the cluster variation method to the fcc Ising ferromagnet

Abstract

The molecular-field-type approximations when applied to the Ising ferromagnet yield inaccurate and sometimes incorrect behaviors at the transition temperature. We have advanced the mathematical approximation of the cluster variation method, which is the generalization of the molecular-field-type approximation, a few more steps so that the four- and six-body correlations are taken into account. Some remarkable features became apparent from preliminary calculations for fcc Ising ferromagnets: (i) The transition temperature is predicted within a few percent of the exact value. ${T}_{c}(4\ensuremath{-}\mathrm{b}\mathrm{o}\mathrm{d}\mathrm{y})=0.83545$, ${T}_{c}(6\ensuremath{-}\mathrm{b}\mathrm{o}\mathrm{d}\mathrm{y})=0.83394$, ${T}_{c}(\mathrm{exact})=0.81627$, with ${T}_{c}(\mathrm{Weiss})=1.00000$; (ii) When closed-form equations for the low-temperature specific heat are expanded into infinite series, all of the known exact coefficients are reproduced; (iii) The extent of mathematical analysis and the amount of numerical computation are considerably less than those involved in diagram enumeration methods.