Activated Aging Dynamics and Effective Trap Model Description in the Random Energy Model

TL;DR

This paper investigates the aging dynamics of the Random Energy Model, demonstrating that an effective trap model accurately describes the long-time evolution but not the initial escape process.

Contribution

It provides a detailed analysis of the REM's aging dynamics, identifying regimes where the trap model applies and explaining the transition between these regimes.

Findings

Trap model accurately describes long-time aging dynamics

Initial escape dynamics do not follow the trap model

Two distinct time regimes identified in REM aging

Abstract

We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.