Statics and dynamics of the ten-state nearest-neighbor Potts glass on the simple-cubic lattice

TL;DR

This study uses Monte Carlo simulations to analyze two Potts glass models on a cubic lattice, finding no static phase transition at nonzero temperatures and revealing dynamic heterogeneity and cluster-based relaxation behaviors.

Contribution

It provides the first detailed simulation-based evidence that short-range Potts glasses lack static phase transitions and exhibit complex dynamic properties.

Findings

No static phase transition at nonzero temperature.

Relaxation times follow Arrhenius law with cluster-based activation energies.

System exhibits dynamic heterogeneity and short correlation lengths.

Abstract

We present the results of Monte Carlo simulations of two different Potts glass models with short range random interactions. In the first model a \pm J-distribution of the bonds is chosen, in the second model a Gaussian distribution. In both cases the first two moments of the distribution are chosen to be J_0=-1, Delta J=+1, so that no ferromagnetic ordering of the Potts spins can occur. We find that for all temperatures investigated the spin glass susceptibility remains finite, the spin glass order parameter remains zero, and that the specific heat has only a smooth Schottky-like peak. These results can be understood quantitatively by considering small but independent clusters of spins. Hence we have evidence that there is no static phase transition at any nonzero temperature. Consistent with these findings, only very minor size effects are observed, which implies that all correlation lengths of the models remain very short. We also compute for both models the time auto-correlation function C(t) of the Potts spins. While in the Gaussian model C(t) shows a smooth uniform decay, the correlator for the \pm J model has several distinct steps. These steps correspond to the breaking of bonds in small clusters of ferromagnetically coupled spins (dimers, trimers, etc.). The relaxation times follow simple Arrhenius laws, with activation energies that are readily interpreted within the cluster picture, giving evidence that the system does not have a dynamic transition at a finite temperature. Hence we find that for the present models all the transitions known for the mean-field version of the model are completely wiped out. Finally we also determine the time auto-correlation functions of individual spins, and show that the system is dynamically very heterogeneous.