Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study

TL;DR

This study investigates the critical behavior of short-range Potts spin glasses in 3D and 4D using Monte Carlo simulations, revealing phase transitions for p=3 but not for p=10 in 3D.

Contribution

It provides new insights into the critical dimensions and phase transition behavior of short-range Potts glasses with different p-values.

Findings

3D p=3 Potts glass transitions at specific T_c values

No transition observed for p=10 in 3D

4D p=3 Potts glass exhibits a phase transition at T_c=0.536

Abstract

We study the critical behavior of the short-range p-state Potts spin glass in three and four dimensions using Monte Carlo simulations. In three dimensions, for p = 3, a finite-size scaling analysis of the correlation length shows clear evidence of a transition to a spin-glass phase at T_c = 0.273(5) for a Gaussian distribution of interactions and T_c = 0.377(5) for a bimodal distribution. These results indicate that the lower critical dimension of the 3-state Potts glass is below three. By contrast, the correlation length of the ten-state (p = 10) Potts glass in three dimensions remains small even at very low temperatures and thus shows no sign of a transition. In four dimensions we find that the p = 3 Potts glass with Gaussian interactions has a spin-glass transition at T_c =0.536(3).