Revisiting the critical behavior of nonequilibrium models in Short-time Monte Carlo Simulations

TL;DR

This paper compares two methods for accurately estimating the dynamic critical exponent z in nonequilibrium models like the contact process and Domany-Kinzel automaton using short-time Monte Carlo simulations.

Contribution

It introduces and evaluates two alternative approaches for determining the exponent z, enhancing the reliability of short-time dynamic analysis in nonequilibrium models.

Findings

Both methods yield consistent estimates of z.

The methods are effective with short-time simulation data.

Additional estimates of ν_{||} are obtained using Grassberger's method.

Abstract

We analyze two alternative methods for determining the exponent $z$ of the contact process (CP) and Domany-Kinzel (DK) cellular automaton in Monte Carlo Simulations. One method employs mixed initial conditions, as proposed for magnetic models [Phys. Lett. A. \textbf{298}, 325 (2002)]; the other is based on the growth of the moment ratio $m(t)=< \rho ^{2}(t)> /< \rho (t)> ^{2}$ starting with all sites occupied. The methods provide reliable estimates for $z$ using the short time dynamics of the process. Estimates of $\nu_{||}$ are obtained using a method suggested by Grassberger.