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We investigate the critical properties of the four-state commutative randompermutation glassy Potts model in three and four dimensions by means of MonteCarlo simulation and of a finite size scaling analysis. Thanks to the use of afield programmable gate array we have been able to thermalize a large number ofsamples of systems with large volume. This has allowed us to observe aspin-glass ordered phase in d=4 and to study the critical properties of thetransition. In d=3, our results are consistent with the presence of aKosterlitz-Thouless transition, but we cannot exclude transient effects due toa value of the lower critical dimension slightly below 3.

Critical properties of the four-state Commutative Random Permutation Glassy Potts model in three and four dimensions