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

TL;DR

This paper investigates the critical dynamics of the 4-state Potts model using short-time Monte Carlo simulations to estimate dynamic and static critical exponents, confirming theoretical conjectures and universality class relations.

Contribution

It introduces new estimates of the dynamic exponent θ and the anomalous dimension x₀ for the 4-state Potts model through short-time simulations, supporting theoretical predictions.

Findings

Estimated dynamic exponents θ₁ and θ₂ consistent with conjectures.

Calculated static exponents β and ν aligning with literature.

Confirmed universality class relation with the 2D Ising model.

Abstract

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 $% x_{0}=z\theta +\beta /\nu $ 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.