Crossover from entropic to thermal dynamics in glassy models

TL;DR

This paper investigates the transition from entropic to thermal dynamics in glassy models, revealing a crossover characterized by singularities, ultrametricity, and complex aging behaviors in finite and generalized models.

Contribution

It introduces a detailed analysis of the entropic-thermal crossover in glassy models, including finite size effects and a generalized model with a threshold energy, uncovering new aging scaling phenomena.

Findings

Short time singularity in correlation functions near Tg

Dynamical ultrametricity at Tg

Presence of multiple aging regimes with non-trivial scaling

Abstract

We study the emergence of a crossover from entropically driven to thermally activated dynamics in different versions of the `entropic' phase space model introduced by Barrat and M\'ezard, and previously considered in the zero temperature limit. We first focus on the low temperature (T < Tg) aging phase of the original model and show that a short time singularity appears in the correlation function for Tg/2 < T < Tg, leading to dynamical ultrametricity at T=Tg. We then consider the finite size version of this model, showing that the long time dynamics is always thermally activated beyond a size dependent crossover time scale. We also generalize the model, introducing a threshold energy so as to mimic a phase space composed of saddles above the threshold, and minima below. In this case, the crossover time scale becomes much smaller than the equilibration time, and both kinds of aging dynamics are successively found, inducing a non trivial aging scaling which does not reduce to the usual t/tw one.