Are mean-field spin-glass models relevant for the structural glass transition?

We analyze the properties of the energy landscape of finite-size fully connected p-spin-like models whose high-temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids. We show that finite-size fully connected p-spin-like models, where activated processes are possible, do exhibit properties typical of real super-cooled liquid when both are near the critical glass transition. Our results support the conclusion that fully connected p-spin-like models are the natural statistical mechanical models for studying the glass transition in super-cooled liquids.