A mean field method with correlations determined by linear response

TL;DR

This paper presents a novel mean-field approximation that combines maximum entropy and linear response to better estimate correlations, improving upon existing methods like Bethe and Sessak-Monasson, especially at high temperatures.

Contribution

The paper introduces a new mean-field method that enhances correlation estimates by integrating maximum entropy with linear response, generalizing previous approaches.

Findings

Improved correlation estimates over Bethe approximation.

Enhanced performance in direct and inverse Ising problems.

Better accuracy at high temperatures.

Abstract

We introduce a new mean-field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method. Within a general formalism that includes previous mean-field methods, we derive formulas improving upon, e.g., the Bethe approximation and the Sessak-Monasson result at high temperature. Applying the method to direct and inverse Ising problems, we find improvements over standard implementations.