On Mean Field Glassy Dynamics out of Equilibrium

TL;DR

This paper investigates the out-of-equilibrium dynamics of mean field disordered systems, revealing coexistence of equilibrium and aging regimes with a hierarchical crossover structure.

Contribution

It provides analytical and numerical analysis of off-equilibrium dynamics in spin glasses, highlighting the hierarchical aging behavior and crossover phenomena.

Findings

Coexistence of equilibrium and aging regimes in spin glass dynamics

Hierarchical structure of crossovers between observation and waiting times

Validation through analytical and numerical methods

Abstract

We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a low temperature spin glass phase with continuous replica symmetry breaking. We study the equations of off equilibrium dynamics with analytical and numerical methods. In the spin glass phase, we find that the usual equilibrium dynamics (observed when the observation time is much smaller than the waiting time) coexists with an aging regime. In this aging regime, we propose a solution implying a hierarchy of crossovers between the observation time and the waiting time.