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

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.Comment: 65 pages, 15 figures. Uses lprocl.sty (included). This article will appear in `Spin-glasses and random fields', A. P. Young Ed. (World Scientific