Absence of Replica Symmetry Breaking in Finite Fifth Moment Random Field Ising Model

TL;DR

This paper proves that in the Random Field Ising Model with finite fifth moment disorder, replica symmetry does not break in any dimension, temperature, or field strength, almost surely.

Contribution

It establishes the absence of replica symmetry breaking in the RFIM with finite fifth moment disorder across all dimensions and parameters, a significant theoretical advancement.

Findings

No replica symmetry breaking occurs in the model.

Results hold for all dimensions, temperatures, and field strengths.

Almost sure absence of replica symmetry breaking.

Abstract

This work is concerned with the theory of the Random Field Ising Model on the hypercubic lattice, in the presence of a independent disorder with finite fifth moment. We showed the absence of replica symmetry in any dimensions, at any temperature and field strength, almost surely.