Glassy transition in the three-dimensional random field Ising model

TL;DR

This paper investigates the high-temperature behavior of the 3D random field Ising model, revealing a glassy phase between the ferromagnetic and paramagnetic phases using replica symmetry breaking.

Contribution

It introduces a replica symmetry breaking analysis to identify a glassy phase in the 3D RFIM, extending understanding of its phase diagram.

Findings

Glassy phase exists between T_f and T_b

Correlation length at T_b matches previous numerical results

Paramagnetic phase occurs only above T_b

Abstract

The high temperature phase of the three dimensional random field Ising model is studied using replica symmetry breaking framework. It is found that, above the ferromagnetic transition temperature T_f, there appears a glassy phase at intermediate temperatures T_f<T<T_b while the usual paramagnetic phase exists for T>T_b only. Correlation length at T_b is computed and found to be compatible with previous numerical results.