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Chinese Physics Letters

Dynamic Scaling and Universality of the Two-Dimensional Random-Bond Potts Model

Ying He-Ping, Bian Bao-Jun, JI DA-REN, Lothar Schülke

Published Sep 19, 2001• 2 citations
Publisher

Abstract

Short-time dynamics and universality are investigated for the random-bond Potts model with a trinary distribution of quenched randomness on a two-dimensional triangular lattice. The universal power-law scaling behaviour is applied to estimate the exponents z and β/ν. Emphasis is placed on dynamic Monte Carlo evolutions for different multi-disorder amplitudes. Our results indicate that the quenched impurities cause a change of the critical universality.

DOI
10.1088/0256-307x/18/10/334

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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≈0.54 in the pure system to z≈0.24 at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain γ/ν≈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.