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

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.