Potential energy landscape of finite-size mean-field models for glasses

Abstract

We analyze the properties of the energy landscape of finite-size fullyconnected spin-glass models with a discontinuous transition. In thethermodynamic limit the equilibrium properties in the high-temperaturephase are described by the schematic mode coupling theory ofsuper-cooled liquids. We show that finite-size fullyconnected spin-glass models do exhibit properties typical ofLennard-Jones systems when both are near the critical glass transition,where thermodynamics is ruled by energy minima distribution. Ourstudy opens the way to consider activated processes in real glassesthrough finite-size corrections (i.e. calculations beyond the saddle-point approximation) in mean-field spin-glass models.