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Journal of Chongqing University of Arts and Sciences

The dynamic exponent of two-dimensional eight-state Potts model

Lei Xiao-wei

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

With a large-scale Monte Carlo simulation,the two-dimensional eight-state Potts model of square lattice is investigated.Starting from an ordered initial state,the dynamic evolution of the Binder cumulant is studied.Based on dynamic scaling ansatz,the dynamic exponent z is determined with relatively high accuracy.It is clear that z depends on the disorder amplitude and is much bigger than that of the two-dimensional Ising model.The two-dimensional random-bond Potts model is not in the same dynamic universality class as the two-dimensional Ising model.

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With a large-scale Monte Carlo simulation,the two-dimensional eight-state Potts model of square lattice is investigated.Starting from an ordered initial state,the dynamic evolution of the Binder cumulant is studied.Based on dynamic scaling ansatz,the dynamic exponent z is determined with relatively high accuracy.It is clear that z depends on the disorder amplitude and is much bigger than that of the two-dimensional Ising model.The two-dimensional random-bond Potts model is not in the same dynamic universality class as the two-dimensional Ising model.
The short-time critical dynamics of the two-dimensional eight-state random-bond Potts model is investigated with large-scale Monte Carlo simulations. Dynamic relaxation starting from a disordered and an ordered state is carefully analyzed. The continuous phase transition induced by disorder is studied, and both the dynamic and static critical exponents are estimated. The static exponent beta/nu shows little dependence on the disorder amplitude r, while the dynamic exponent z and static exponent 1/nu vary with the strength of disorder.
With a large-scale Monte Carlo simulation, non-equilibrium dynamics of the two-dimensional fully frustrated XY model is investigated. We tackle the Kosterlitz-Thouless phase transition. Starting from an ordered initial state, we study the dynamic evolution of the magnetization as well as a specifically defined Binder cumulant. From the dynamic scaling ansatz, we extract the correlating time of the dynamics and the spatial correlation length of the equilibrium state. The dynamic exponent z is determined with relatively high accuracy. Especially, we suggest and demonstrate how one may directly measure the dynamic exponent z above TKT from the scaling fit of the Binder cumulant. These results indicate that the dynamic exponent z fluctuates around z=2, and this is consistent with that observed at temperatures below the transition temperature TKT.
Critical scaling and universality in short-time dynamics for spin models on a twodimensional triangular lattice are investigated by using Monte Carlo simulation. Emphasis is placed on the dynamic evolution from fully ordered initial states to show that universal scaling exists already in the short-time regime in form of power-law behavior of the magnetization and Binder cumulant. The results measured for the dynamic and static critical exponents, θ, z, β and ν, confirm explicitly that the Potts models on the triangular lattice and square lattice belong to the same universality class. Our critical scaling analysis strongly suggests that the simulation for the dynamic relaxation can be used to determine numerically the universality.
We present an extensive Monte Carlo study of the critical relaxation for the two-dimensional square lattice random-bond Potts model using Swendsen-Wang cluster flipping. The integrated autocorrelation time \ensuremath{\tau} is calculated and the dynamic exponent z is estimated by analyzing the size dependence of \ensuremath{\tau}. We find that z\ensuremath{\approx}0 in agreement with estimates for the two-dimensional Ising model. We also present a study of the size dependence of the dynamic behavior of the pure eight-state Potts model which undergoes a first-order transition. The scaling is describable by the product of an exponential times a power law, a behavior which is quite different from that found in the random-bond case.