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

We analyze the properties of the energy landscape of finite-size fully connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high-temperature phase are described by the schematic mode coupling theory of super-cooled liquids. We show that finite-size fully connected spin-glass models do exhibit properties typical of Lennard-Jones systems when both are near the critical glass transition, where thermodynamics is ruled by energy minima distribution. Our study opens the way to consider activated processes in real glasses through finite-size corrections (i.e. calculations beyond the saddle-point approximation) in mean-field spin-glass models.