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We study the dynamics of the q-state random bond Potts ferromagnet on thesquare lattice at its critical point by Monte Carlo simulations with singlespin-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 distributionof relaxation times among different samples, finding different results for thetwo q values. For q=3 the relative variance of the relaxation time tau at thecritical point is finite. However, for q=24 this appears to diverge in thethermodynamic limit and it is ln(tau) which has a finite relative variance. Wespeculate that this difference occurs because the transition of thecorresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio

Critical behavior and lack of self-averaging in the dynamics of the random Potts model in two dimensions