The dynamics of disordered systems, in particular spin glasses, shows very peculiar features that appear very untypical from what one is used to in Markovian dynamics. Rather than exponentially decaying to an equilibrium state, one observes power law behaviour that has become known as “aging” in the physics literature. It is generally believed that such slow down of the dynamics is linked in this systems to a complicated structure of metastable state. Over the last years this phenomenon has been heavily investigated both numerically and, on a very heuristic level, in simple toy models. One of the most common toy models, the so called “REM-like trap model”, introduced by Bouchaud, is in turn supposed to mimic the behaviour of the simplest spin glass model, the random energy model (REM) of Derrida. In this talk I report on joint work with G. Ben Arous and V. Gayrard in which aging is analysed in a rigorous way for the actual Glauber dynamics of the REM. Our approach uses precise control on transitions of the process between a selected set of “metastable” states.
This uses techniques developed recently in collaboration with M. Eckhoff, V. Gayrard, and M. Klein which I will review briefly. References