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. In recent years a significant effort has been devoted to the understanding of glass-forming systems. Recent theoretical and numerical results clearly show that the slowing down of the dynamics is strongly connected to the potential energy landscape. The trajectory of the representative point in the configuration space can be viewed as a path in a multidimensional potential energy surface. The dynamics is therefore strongly influenced by the topography of the potential energy landscape: local minima, barriers heights, basin of attraction and other topological properties all influence the dynamics. The potential energy surface of a super-cooled liquid contains a large number of local minima, called inherent structures (IS) [1], each surrounded by a basin defined as the set of all configurations that a local energy minimization maps onto the IS contained within it. In this picture the time evolution of the system can be divided into intra-basin and inter-basinmotion. Transition from one basin to another are expected to occur differently as the temperature is varied. In particular, when the temperature is lowered down to the order of the critical Mode Coupling Theory (MCT) temperature TMCT the two motions become well separated in time (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]