An alternative order parameter for the 4-state Potts model

TL;DR

This paper explores a new order parameter for the 4-state Potts model to analyze its dynamic critical behavior, estimating key exponents and confirming consistency with existing literature.

Contribution

It introduces an alternative order parameter for the 4-state Potts model and demonstrates its effectiveness in estimating critical exponents.

Findings

Estimated the global persistence exponent $ heta_g$.

Obtained critical exponents $ heta$, $z$, $ u$, and $eta$.

Results agree with established literature values.

Abstract

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.