Static and dynamic glass transitions in the 10-state Potts glass: What can Monte Carlo simulations contribute?

The p-state Potts glass with infinite range Gaussian interactions can be solved exactly in the thermodynamic limit and exhibits an unconventional phase behavior if p>4: A dynamical transition from ergodic to non-ergodic behavior at a temperature T_D is followed by a first order transition at T₀<T_D, where a glass order parameter appears discontinuously, although the latent heat is zero. If one assumes that a similar scenario occurs for the structural glass transition as well (though with the singular behavior at T_D rounded off), the p-state Potts glass should be a good test case to develop methods to deal with finite size effects for the static as well as the dynamic transition, and to check what remnants of these unconventional transitions are left in finite sized systems, as they are used in simulations. While it is shown that a sensible extrapolation N→∞ of the simulation results are compatible with the exact results, we find that it would be rather difficult to obtain a correct understanding of the behavior of the system in the thermodynamic limit if only the numerical data would be available.