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Acta Physica Sinica

A study on critical universality of the random-bond Potts models with self-dual quenched randomness

Ren Hao, Gu De-Wei, Pan Zheng-Quan, Ying He-Ping, (1)杭州成人科技大学,杭州 310006; (2)浙江大学物理系, 浙江近代物理中心,杭州 310027

Published Jan 1, 2004• 0 citations
Publisher

Abstract

In this paper we present our numerical study on short-time critical dynamics for the q-state random-bond Potts model with self-dual quenched disorders. By exploring the universal power-law scaling behavior, the results of magnetic exponent η and dynamic exponent z are estimated for the q=3 and q=8 cases with two specific disorder distribution functions. Our Monte Carlo simulations show evidence that the results of magnetic exponent η are independent of distribution forms, which verifies the existence of universality for the general quenched random-bond models numerically.

DOI
10.7498/aps.53.265

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In this paper we present our numerical study on short-time critical dynamics for the q-state random-bond Potts model with self-dual quenched disorders. By exploring the universal power-law scaling behavior, the results of magnetic exponent η and dynamic exponent z are estimated for the q=3 and q=8 cases with two specific disorder distribution functions. Our Monte Carlo simulations show evidence that the results of magnetic exponent η are independent of distribution forms, which verifies the existence of universality for the general quenched random-bond models numerically.
We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent z and magnetic exponent η, as well as the exponent θ. Our special attention is paid to the dynamic process for the q = 8 Potts model.
Critical behavior in short-time dynamics is investigated by a Monte Carlo study for the random-bond Potts ferromagnet with a trinary distribution of quenched disorders on two-dimensional triangular lattices. The dynamic scaling is verified and applied to estimate critical exponents θθθ, zzz and β/νβ/νβ/ν for several realizations of the trinary distribution. Our critical scaling analysis strongly indicates that the bond randomness influences the critical universality.
We present results of Monte Carlo simulations of random bond Potts models in two dimensions, for different numbers of Potts states q. We introduce a simple scheme which yields continuous self-dual distributions of the interactions. As expected, we find multifractal behavior of the correlation functions at the critical point and obtain estimates of the exponent ${\ensuremath{\eta}}_{n}$ for several moments n of the correlation functions, including typical $(\stackrel{\ensuremath{\rightarrow}}{n}0)$, average (n=1)(n=1)(n=1), and others. In addition, for q=8q=8q=8, we find that there is only a single correlation length exponent $\ensuremath{\nu}$ describing the correlation length away from criticality. This is numerically very close to the pure Ising value $\ensuremath{\nu}=1$.