Activated dynamics: An intermediate model between the random energy model and the p-spin model.

To study the activated dynamics of mean-field glasses, which takes place on times of order exp(N), where N is the system size, we introduce a new model, the correlated random energy model (CREM), that allows for a smooth interpolation between the REM and the p-spin models. We study numerically and analytically the CREM in the intermediate regime between REM and p-spin. We fully characterize its energy landscape, which is like a golf course but, at variance with the REM, has metabasins (or holes) containing several configurations. We find that an effective description for the dynamics, in terms of traps, emerges, provided that one identifies metabasins in the CREM with configurations in the trap model.