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

TL;DR

This study compares the short-time critical dynamics of the Baxter-Wu, Turban, and four-state Potts models, introducing a new exponent to distinguish their critical behaviors and revisiting existing dynamical exponents.

Contribution

It introduces the global persistence exponent as a new tool for differentiating critical behaviors and provides updated estimates of dynamical exponents for these models.

Findings

The global persistence exponent effectively distinguishes models' critical behaviors.

Updated dynamical exponents for the four-state Potts model are provided.

The anomalous dimension of initial magnetization may be zero for the Turban model.

Abstract

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.