Absence of replica symmetry breaking in the random field Ising model

TL;DR

This paper proves that the random field Ising model does not exhibit replica symmetry breaking across all dimensions, temperatures, and field strengths, except for possibly a negligible set of special conditions.

Contribution

It establishes the absence of replica symmetry breaking in the random field Ising model in all dimensions and conditions, except for a measure-zero set of exceptions.

Findings

Replica symmetry is not broken in the model in any dimension.

The result holds at all temperatures and field strengths.

Exceptions, if any, are confined to a measure-zero set of parameters.

Abstract

It is shown that replica symmetry is not broken in the random field Ising model in any dimension, at any temperature and field strength, except possibly at a measure-zero set of exceptional temperatures and field strengths.