Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses

Abstract

We investigate the Inherent Structure (IS) dynamics of mean-field finite-size spin-glass models whose high-temperature dynamics isdescribed in the thermodynamic limit by the schematic Mode CouplingTheory for supercooled liquids. Near the threshold energy the dynamicsis ruled by activated processes which induce a logarithmic slowrelaxation. We show the presence of aging in both the IS correlation andintegrated response functions and check the validity of the one-stepreplica symmetry breaking scenario in the presence of activatedprocesses. Our work shows: 1) the violation of thefluctuation-dissipation theorem can be computed from the configurational entropy obtained in the Stillinger and Weberapproach,2) the intermediate time regime (log (t) ∼ N) in mean-field theory automatically includes activated processesopening the way to analytically investigate activated processes bycomputing corrections beyond mean field.