Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different ‘susceptibilities’ to temperature changes, for the free-energy and for other (‘magnetic’) observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1− T/Tc) for the free-energy. A small temperature change in the low temperature phase of spin-glasses is able to ‘rejuvenate’ an already aged system [1, 2, 3]. More precisely, the a.c. susceptibility of a system aged for a very long time at T1 < Tc (where Tc is the spin-glass phase transition temperature) and then suddenly cooled at T1 − ∆T is, provided ∆T is not too small, very close the the susceptibility of a young system directly cooled from high temperatures to T1 −∆T . This ‘fragility’ to temperature changes has been interpreted early on as a signature of ‘temperature chaos’, that is the fact that the equilibrium states of a disordered system are very different for different temperatures: beyond a certain