Dynamical Critical Properties of the Random-Bond three-state Potts Model

Abstract

We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen--Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent $z$ via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from $z \approx 0.54$ in the pure system to $z \approx 0.24$ at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain $γ/ν\approx 1.73$, where $γ$ and $ν$ are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.