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

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.

Keywords:

• ergodicity and thermodynamic homogeneity
• replications of phase space
• mean-field theory of spin glasses
• discrete and continuous replica-symmetry breaking
• asymptotic solutions with broken replica symmetry

Disclosure statement

No potential conflict of interest was reported by the authors.