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

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

2007-10-23

arxiv.org/abs/0710.4246v2

Phys. Rev. B 77, 104432 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 8 Postscript figures

Scientific paper

10.1103/PhysRevB.77.104432

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 programmable 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.

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