Aging and spin-glass dynamics

TL;DR

This paper reviews recent mathematical findings on aging phenomena in simple disordered models like the Bouchaud trap model and spin-glass models, highlighting differences in aging behaviors across models and time scales.

Contribution

It provides a comprehensive survey of recent mathematical results on aging in disordered models, emphasizing phenomenological differences across models and time scales.

Findings

Different models exhibit distinct aging phenomenology.

The REM is well approximated by the Bouchaud model on the complete graph.

Various models show different aging behaviors depending on time scales.

Abstract

We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy Model, which is well approximated by the Bouchaud model on the complete graph), then the spherical Sherrington-Kirkpatrick model. We will insist on the differences in phenomenology for different types of aging in different time scales and different models. This talk is based on joint works with A.Bovier, J.Cerny, A.Dembo, V.Gayrard, A.Guionnet, as well as works by C.Newman, R.Fontes, M.Isopi, D.Stein.