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

TL;DR

This study uses Monte Carlo simulations and finite size scaling to explore the critical properties of a four-state glassy Potts model in three and four dimensions, revealing a spin-glass phase in four dimensions and suggesting a Kosterlitz-Thouless transition in three.

Contribution

First large-scale simulation of the four-state commutative random permutation glassy Potts model in 3D and 4D, identifying critical behaviors and phase transitions.

Findings

Spin-glass phase observed in 4D

Kosterlitz-Thouless transition suggested in 3D

Large system sizes enabled by FPGA acceleration

Abstract

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.