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

– We investigate the inherent structure (IS) dynamics of mean-field finite-size spin-glass models whose high-temperature dynamics is described in the thermodynamic limit by the schematic Mode Coupling Theory for super-cooled liquids. Near the threshold energy the dynamics is ruled by activated processes which induce a logarithmic slow relaxation. We show the presence of aging in both the IS correlation and integrated response functions and check the validity of the one-step replica symmetry breaking scenario in the presence of activated processes. Our work shows: 1) The violation of the fluctuation-dissipation theorem is given by the configurational entropy, 2) The intermediate time regime (log(t) ∼ N) in mean-field theory automatically includes activated processes opening the way to analytically investigate activated processes by computing corrections beyond mean-field. After many years of research on the structural glass problem a lot of experimental data has been collected but a convincing theory is still needed [1, 2]. The two most successful theories for the glass transition are the Adam-Gibbs-DiMarzio and the ideal Mode Coupling Theory (MCT) [3]. Despite their different character both are mean-field theories. In the former case the mean-field aspect lies in the notion of configurational entropy which assumes a breaking of the phase space in disconnected ergodic components. In the latter the presence of the MCT transition marks the onset of ergodicity breaking where the diverging of a characteristic time occurs. Both approaches have been successfully unified in the context of spin-glass theories [4]. To go beyond mean-field it is necessary to include activated processes, a very difficult task since it implies the knowledge of the excitations involved in the dynamics. Recent theoretical and numerical results clearly show that the slowing down of the dynamics near the structural glass transition is strongly connected to the complex topology of the potential energy landscape [5]. In a glass-forming systems this is made by many deep valleys connected by saddles. The (∗) e-mail:[email protected] (∗∗) e-mail:[email protected]