We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulation and of a finite size scaling analysis. Thanks to the use of a field programmabl
e gate array we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but we cannot exclude transient effects due to a value of the lower critical dimension slightly below 3.
