Résumé
It is still an unsolved problem whether or not there is a static phase transition from a (metastable) supercooled fluid to a (metastable) ideal glass underlying the structural glass transition, or whether the latter is purely a dynamical transition (such as described by mode coupling theory). The p-state infinite range Potts glass with p > 4 is known as an example where both a static and a dynamic transition occur in the thermodynamic limit, N --> infinity. In the present paper, we use Monte Carlo simulations to study for the case p = 10 how this limit is approached by considering values of N in the range 160 less than or equal to N less than or equal to 2560. While the mean-field scenario is recovered qualitatively, unexpectedly large finite-size effects are found. Near the dynamic transition, evidence for dynamic finite size scaling is found, but the exponents describing the N-dependence of the relaxation time and other quantities are not understood analytically. The extent to which this model can mimic the glass transition of real systems is discussed.