  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 {\it 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.
