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arXiv · 1612.05842

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

H. A. Fernandes·R. da Silva·A. A. Caparica·J. R. Drugowich de Felício
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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 $θ_{m}$ and $θ_{p}$, related to the magnetic and electric order parameters, as well as the persistence exponent $θ_{g}$, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent $z$ and the static critical exponents $β$ and $ν$ 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 $β/ν$ exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

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H. A. Fernandes, R. da Silva, A. A. Caparica, J. R. Drugowich de Felício. 2016-12-18. Non-equilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line. https://doi.org/10.1103/physreve.95.042105

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