Elusive Glassy Phase in the Random Field Ising Model

TL;DR

This paper proves that the random field Ising model cannot have a spin glass phase at equilibrium outside the ferromagnetic critical line, but a glassy phase may exist when magnetization is constrained.

Contribution

It provides a rigorous proof ruling out equilibrium spin glass phases in the RFIM outside the ferromagnetic critical line and demonstrates the existence of a glassy phase under fixed magnetization.

Findings

Spin glass susceptibility is bounded by ferromagnetic susceptibility.

No equilibrium spin glass phase exists outside the ferromagnetic critical line.

A glassy phase can exist when magnetization is fixed below equilibrium value.

Abstract

We consider the random field Ising model and show rigorously that the spin glass susceptibility at equilibrium is always bounded by the ferromagnetic susceptibility, and therefore that no spin glass phase can be present at equilibrium out of the ferromagnet critical line. When the magnetization is, however, fixed to values smaller than the equilibrium one, a glassy phase can exist, as we show explicitly on the Bethe lattice.