Non-equilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

TL;DR

This study explores the short-time critical dynamics of the 2D Ashkin-Teller model at the Baxter line using Monte Carlo simulations, estimating critical exponents and confirming universality of certain ratios.

Contribution

It introduces a refined method for estimating static exponents and provides comprehensive dynamic critical exponent estimates at the Baxter line.

Findings

Critical parameters obtained via power law decay of magnetization.

Universal behavior of the ratio β/ν along the critical line.

Consistent estimates of dynamic exponents using bootstrap and averaging methods.

Abstract

We investigate the short-time universal behavior of the two dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo Simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power law decay of the magnetization. Thus, the dynamic critical exponents $\theta _{m}$ and $\theta _{p}$, related to the magnetic and electric order parameters, as well as the persistence exponent $\theta _{g}$, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent $z$ and the static critical exponents $\beta $ and $\nu $ for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another which is taken over geographic variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio $\beta /\nu $ exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.