Résumé
The question whether there is a static phase transition underlying the freezing of a supercooled fluid into a glass, or a purely dynamical transition (such as described by the mode-coupling theory of the glass transition) is briefly reviewed. The mean-field Potts glass with p > 4 states provides a model where both a static and a dynamic transition occur. We describe Monte Carlo simulations which provide insight into the behavior of this model and discuss how these transitions show up in systems of finite size. By studying a 10-state Potts glass with nearest-neighbor interactions on the simple cubic lattice, evidence is obtained that even at very low temperatures only short range order due to small clusters of strongly correlated Potts spins is possible. No trace of the static and dynamic glass transition found in the mean-field limit is left. Possibilities to construct models which better describe the phenomena at the glass transition of real materials are briefly discussed.