Out of equilibrium dynamics in spin-glasses and other glassy systems

TL;DR

This paper reviews recent theoretical advances in understanding glassy dynamics, emphasizing the aging regime's universality across various models and experimental contexts, and discusses open problems linking mean-field and finite-dimensional systems.

Contribution

It synthesizes phenomenological, analytical, and simple non-disordered models of glassy dynamics, highlighting their interrelations and identifying key open questions.

Findings

Universal features of aging in glassy systems

Analytical results for mean-field low-temperature dynamics

Connections between different modeling approaches

Abstract

We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i) Phenomenological models of aging (coarsening, trap models), (ii) Analytical results for the low-temperature dynamics of mean-field models (corresponding to the mode-coupling equations); and (iii) Simple non-disordered models with glassy dynamics. We discuss the interrelation between these approaches, and also with previous work in the field. Several open problems are underlined -- in particular the precise relation between mean-field like (or mode-coupling) descriptions and finite dimensional problems.