Universality of random energy model-like ageing in mean field spin glasses

Ageing has become the paradigm for describing dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of the effective dynamics of such systems. In this Letter we show that in a wide class of mean field models and on a wide range of time scales, ageing occurs precisely as predicted by the random energy model-like trap model of Bouchaud and Dean. This is the first rigorous result concerning ageing in mean field models other than the random energy model and the spherical model.