Critical dynamics of the Potts model: short-time Monte Carlo simulations

We calculate the new dinamic exponent $\theta$ of the 4-state Potts model, using short-time simulations. Our estimates $\theta_{1}=-0.0471(33)$ and $\theta_{2}=$ $-0.0429(11)$ obtained by following the behavior of the magnetization or measuring the evolution of the time correlation function of the magnetization corroborate the conjecture by Okano et. al. In addition, these values agree with previous estimate of the same dynamic exponent for the two-dimensional Ising model with three-spin interactions in one direction, that is known to belong to the same universality class as the 4-state Potts model. The anomalous dimension of initial magnetization $$ is calculated by an alternative way that mixes two different initial conditions. We have also estimated the values of the static exponents $\beta$ and $\nu$. They are in complete agreement with the pertinent results of the literature.Comment: 12 pages, 7 figure

An alternative order parameter for the 4-state Potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. \textbf{20}, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent $\theta_g$ by following the time evolution of the probability $P(t)$ that the considered order parameter does not change its sign up to time $t$. We have also obtained the critical exponents $\theta$, $z$, $\nu$, and $\beta$ using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.Comment: 6 pages, 6 figure

A comparative study of the dynamic critical behavior of the four-state Potts like models

We investigate the short-time critical dynamics of the Baxter-Wu (BW) and $n=3$ Turban (3TU) models to estimate their global persistence exponent $\theta _{g}$. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We also revisit the short-time dynamics of the 3TU model in order to check if, as already found for the FSP model, the anomalous dimension of the initial magnetization $x_{0}$ could be equal to zero