Quadratic short-range order corrections to the mean-field free energy

TL;DR

This paper introduces a quadratic correction method for the free energy in order-disorder systems, improving the accuracy of transition temperature predictions for cubic Ising ferromagnets.

Contribution

It presents a novel quadratic approximation for short-range order corrections using cumulant expansion, applicable to various phases and interactions.

Findings

Enhanced transition temperature estimates for cubic Ising ferromagnets.

Second-order correlation corrections improve mean-field free energy calculations.

Method applicable to arbitrary thermodynamic phases and interaction types.

Abstract

A method for calculating the short-range order part of the free energy of order-disorder systems is proposed. The method is based on the apllication of the cumulant expansion to the exact configurational entropy. Second-order correlation corrections to the mean-field approximation for the free energy are calculated for arbitrary thermodynamic phase and type of interactions. The resulting quadratic approximation for the correlation entropy leads to substantially better values of transition temperatures for the nearest-neighbour cubic Ising ferromagnets.