Modified Mean Field approximation for the Ising Model

TL;DR

This paper introduces a modified mean-field approximation for the Ising Model that considers an infinite chain of spins, significantly improving accuracy with minimal additional computational effort.

Contribution

It proposes a novel approach using an infinite chain of spins coupled to the mean field, enhancing the traditional mean-field approximation for the Ising Model.

Findings

Improved accuracy over standard mean-field methods

Efficient computational approach

Applicable in arbitrary dimensions

Abstract

We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.