Weighted Mean Field Theory for the Random Field Ising Model

TL;DR

This paper develops a weighted mean field theory for the 3D Random Field Ising Model, revealing critical behavior and calculating critical exponents through numerical solutions.

Contribution

It introduces a novel weighted mean field approach that accounts for multiple solutions, providing new insights into the critical phenomena of the model.

Findings

Critical behavior observed from weighted sum of solutions

Critical exponents calculated numerically

Method applied specifically to three dimensions

Abstract

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe critical behavior arising from the weighted sum. The resulting exponents are calculated.