Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions

Abstract

We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.