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arXiv:1612.05842 · Physical review. E

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

Henrique A. Fernandes, Roberto da Silva, Álvaro A. Caparica, J. R. Drugowich de Felício

Published Apr 5, 2017• 9 citations
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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 temporal 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.

DOI
10.1103/physreve.95.042105

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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 temporal 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.
In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.
We have investigated the dynamic critical behavior of the two-dimensional Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We have obtained estimates of some critical points in its rich phase diagram and included, among the usual critical lines the study of first-order (weak) transition by looking into the order-disorder phase transition. In addition, we also investigated the soft-disorder phase transition by considering empiric methods. A study of the behavior of β/νz along the self-dual critical line has been performed and special attention has been devoted to the critical bifurcation point, or Fateev-Zamolodchikov (FZ) point. First, by using a refinement method and taking into account simulations out of equilibrium, we were able to localize parameters of this point. In a second part of our study, we turned our attention to the behavior of the model at the early stage of its time evolution in order to find the dynamic critical exponent z as well as the static critical exponents β and ν of the FZ point on square lattices. The values of the static critical exponents and parameters are in good agreement with the exact results, and the dynamic critical exponent z≈2.28 very close to the four-state Potts model (z≈2.29).
Critical scaling and universality in short-time dynamics for spin models on a twodimensional triangular lattice are investigated by using Monte Carlo simulation. Emphasis is placed on the dynamic evolution from fully ordered initial states to show that universal scaling exists already in the short-time regime in form of power-law behavior of the magnetization and Binder cumulant. The results measured for the dynamic and static critical exponents, θ, z, β and ν, confirm explicitly that the Potts models on the triangular lattice and square lattice belong to the same universality class. Our critical scaling analysis strongly suggests that the simulation for the dynamic relaxation can be used to determine numerically the universality.
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The short-time behavior of the Baxter-Wu model is investigated through the relaxation of the order parameter at the critical temperature. We considered Monte Carlo simulations for this model on a triangular lattice, and we studied relaxation starting from the fourfold-degenerate ground state. Using the short-time scaling formalism we found the static critical exponents beta and nu of the model and the corresponding dynamical critical exponent z. The values of the static exponents we find agree with the exact ones. To the best of our knowledge, this is the first determination of the dynamical critical exponent of the Baxter-Wu model.