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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Critical dynamics of the Baxter-Wu model

M. Santos, W. Figueiredo

Published Mar 19, 2001• 21 citations
Publisher

Abstract

The short-time behavior of the Baxter-Wu model is investigated through the relaxation of the order parameter at the critical temperature. We considered Monte Carlo simulations for this model on a triangular lattice, and we studied relaxation starting from the fourfold-degenerate ground state. Using the short-time scaling formalism we found the static critical exponents beta and nu of the model and the corresponding dynamical critical exponent z. The values of the static exponents we find agree with the exact ones. To the best of our knowledge, this is the first determination of the dynamical critical exponent of the Baxter-Wu model.

DOI
10.1103/physreve.63.042101

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The short-time behavior of the Baxter-Wu model is investigated through the relaxation of the order parameter at the critical temperature. We considered Monte Carlo simulations for this model on a triangular lattice, and we studied relaxation starting from the fourfold-degenerate ground state. Using the short-time scaling formalism we found the static critical exponents beta and nu of the model and the corresponding dynamical critical exponent z. The values of the static exponents we find agree with the exact ones. To the best of our knowledge, this is the first determination of the dynamical critical exponent of the Baxter-Wu model.
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 study the early time behavior of the Baxter-Wu model, an Ising model with three-spin interactions on a triangular lattice. Our estimates for the dynamic exponent z are compatible with results recently obtained for two models which belong to the same universality class of the Baxter-Wu model: the two-dimensional four-state Potts model and the Ising model with three-spin interactions in one direction. However, our estimates for the dynamic exponent theta of the Baxter-Wu model are completely different from the values obtained for those models. This discrepancy could be related to the absence of a marginal operator in the Baxter-Wu 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.
We have used a standard single-spin-flip Monte Carlo method to study the kinetic behavior of the Baxter-Wu model with temperatures T>Tc{T}_{c}Tc​ for both zero impurities and 11.1 at. % quenched, random nonmagnetic site impurities. For the pure model we find that the linear and nonlinear relaxation are described by a dynamic exponent z=\ensuremath{\Delta}/\ensuremath{\nu}=2.0. With the addition of impurities the exponent for the linear relaxation increases to a value of z\ensuremath{\approxeq}2.8 in approximate agreement with the predictions of renormalization-group theory. The nonlinear relaxation in the impure lattice diverges more slowly than the linear relaxation but in a manner which is not completely consistent with proposed scaling theory.
Monte Carlo simulations of the short-time critical dynamics are reviewed. The short-time universal scaling behavior of the dynamic Ising model and Potts model are discussed in detail, while extension and application to more complex systems as the XY model, the fully frustrated XY model and other dynamic systems are also presented. The investigation of the universal behavior of the short-time dynamics not only enlarges the fundamental knowledge on critical phenomena but also, more interestingly, provides possible new ways to determine not only the new critical exponents θ and θ1, but also the traditional dynamic critical exponent z as well as all static critical exponents.