Dynamics within metastable states in a mean-field spin glass

TL;DR

This paper investigates the dynamics within metastable states of a mean-field spin glass, revealing ergodicity breaking and exponential relaxation through a dynamical approach starting from thermalized initial conditions.

Contribution

It introduces a dynamical method to analyze relaxational behavior within metastable states, extending beyond static analysis in spin-glass models.

Findings

Metastable states exhibit true ergodicity breaking.

Relaxation within metastable states is exponential.

Dynamical analysis complements static results.

Abstract

In this letter we present a dynamical study of the structure of metastable states (corresponding to TAP solutions) in a mean-field spin-glass model. After reviewing known results of the statical approach, we use dynamics: starting from an initial condition thermalized at a temperature between the statical and the dynamical transition temperatures, we are able to study the relaxational dynamics within metastable states and we show that they are characterized by a true breaking of ergodicity and exponential relaxation.