Ergodicity breaking in frustrated disordered systems: Replicas in mean-field spin-glass models

TL;DR

This paper explores ergodicity breaking in frustrated disordered systems, particularly spin glasses, and demonstrates how replica symmetry breaking relates to restoring ergodicity in various mean-field models.

Contribution

It provides explicit asymptotic solutions for different spin glass models, illustrating diverse low-temperature behaviors and the role of replica symmetry breaking in ergodicity.

Findings

Replica symmetry breaking indicates ergodicity breaking.

Different models show distinct low-temperature behaviors.

Explicit solutions for Ising, Potts, and p-spin glasses are presented.

Abstract

We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin glasses. We use replicas of the spin variables to test thermodynamic homogeneity of ergodic equilibrium systems. We show that replica-symmetry breaking reflects ergodicity breaking and is used to restore an ergodic state. We then present explicit asymptotic solutions for the Ising, Potts and $p$-spin glasses. Each of the models shows a different low-temperature behavior and the way the replica symmetry and ergodicity are broken.