Dynamical mean-field theory and the aging dynamics

The study of the equilibrium and the out-of-equilibrium dynamics of spin glasses is crucial to understand some of the characterizing properties of disordered systems, including slow relaxation times and aging. The current chapter focuses on recent developments on this relevant topic. In the first part of the chapter, Andrea Crisanti discusses the relation between the equilibrium dynamics of mean-field spin glasses and RSB, briefly reviewing the pioneering ideas of Sommers and Sompolinsky and the subsequent theory by Crisanti, Horner and Sommers. Jorge Kurchan and Silvio Franz focus on the slow out-of-equilibrium glassy dynamics, in both mean-field models and finite-dimensional models, connecting the RSB scheme of Parisi with the concept of multithermalization. Finally, Andrea Maiorano overviews recent results on the presence (and absence) of weak ergodicity breaking in mean-field spin glasses, a pivotal assumption in many theoretical studies focusing on aging.