The Levy spin glass transition

TL;DR

This paper investigates the phase transition in Levy spin glasses, revealing that the spin glass phase is always replica-symmetry-broken, contrary to previous beliefs, and develops a method to analyze the zero cutoff limit.

Contribution

It introduces a way to handle the epsilon to zero limit in Levy spin glasses and determines the de Almeida-Thouless transition temperature with an external field.

Findings

No stable replica-symmetric phase in zero external field

Spin glass phase is always replica-symmetry-broken

Method for analyzing the epsilon to zero limit

Abstract

We determine the phase transition of the Levy spin glass. A regularized model where the coupling constants smaller than some cutoff $\epsilon$ are neglected can be studied by the cavity method for diluted spin glasses. We show how to handle the $\epsilon\to 0$ limit and determine the de Almeida-Thouless transition temperature in presence of an external field. Contrary to previous findings, in zero external field we do not find any stable replica-symmetric spin glass phase: the spin glass phase is always a replica-symmetry-broken phase.