Activated dynamics: an intermediate model between REM and p-spin

TL;DR

This paper introduces the Correlated Random Energy Model (CREM), a new intermediate model for mean-field glasses that bridges REM and p-spin models, providing insights into activated dynamics and energy landscapes.

Contribution

The paper presents the CREM, a novel model that interpolates between REM and p-spin, enabling detailed study of energy landscapes and activated dynamics in mean-field glasses.

Findings

CREM has a golf-course-like energy landscape with metabasins.

An effective trap model describes CREM dynamics.

Metabasins in CREM correspond to configurations in trap models.

Abstract

In order 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 trap-like description for the dynamics emerges, provided that one identifies metabasins in the CREM with configurations in the trap model.