Fluctuating local field method for the disordered Ising model

TL;DR

This paper introduces a Fluctuating Local Field method for calculating thermal properties of disordered classical spin systems, improving accuracy over mean-field theory by accounting for multiple fluctuating modes.

Contribution

The paper develops a FLF approach that effectively captures fluctuations in disordered Ising models, enabling accurate solutions for larger spin clusters.

Findings

Two fluctuating modes suffice for small systems (~24 spins)

More modes improve accuracy for larger systems

Method outperforms traditional mean-field approximations

Abstract

We present a method for computing thermal properties of classical spin clusters with arbitrarily chosen interactions between spins. For such systems, instability channels are \textit{a priori} not known. The method is based on the Fluctuating Local Field (FLF) approach, the effective description of the system with a nonlinear and fluctuating field, and achieves substantial improvements over mean-field theory. We show that two fluctuating modes are sufficient for numerically accurate solution of systems consisting of two dozen spins, while for larger systems it is needed to account for a larger number of fluctuating modes for a full quantitative agreement with the exact solution.