Critical dynamics of the two-dimensional random-bond Potts model with nonequilibrium Monte Carlo simulations

We study two-dimensional q -state random-bond Potts models for both q=8 and q=5 with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of r_{0}=3 , 10, 15, and 20. The correlation length exponent nu increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation alpha=2-dnu and thus indicates no possibility of the activated dynamic scaling. Both r_{0} and q have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.