Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

Silva, Roberto da; Felício, J. R. Drugowich de; Martinêz, Alexandre Souto

doi:10.1103/physreve.85.066707

Cited by 19 publications

(45 citation statements)

References 38 publications

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“…1 by taking into account only the magnetization and the analysis was carried out by using an approach developed in Ref. [41] in the context of generalized statistics. This tool had also been applied successfully to study multicritical points, for example, tricritical points [39] and Lifshitz point of the ANNNI model [40], Z5 model [42] and also in models without defined Hamiltonian [46].…”

Section: Localization Of Critical Points: Power Law Optimizationmentioning

confidence: 99%

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

et al. 2017

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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 θm and θp, related to the magnetic and electric order parameters, as well as the persistence exponent θg, 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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Section: Localization Of Critical Points: Power Law Optimizationmentioning

confidence: 99%

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

et al. 2017

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“…This ratio has proven to be useful for the calculation of the exponent z for the several spin models governed by Boltzmann-Gibbs Statistical Mechanics but its application also includes models with spin-flip based on generalized statistics [44]. In this technique, graphs of ln F 2 against ln t lay on the same straight line for different lattice sizes, without any re-scaling in time, yielding more precise estimates for z.…”

Section: B Non-equilibrium Critical Dynamicsmentioning

confidence: 99%

Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model

2013

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In this work, we study the critical behavior of second order points and specifically of the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions (ANNNI model), using time-dependent Monte Carlo simulations. First of all, we used a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time: M m 0 =1 ∼ t −β/νz which is expected of simulations starting from initially ordered states. Secondly, we obtain original results for the dynamic critical exponent z, evaluated from the behavior of the ratio F2(t) = M 2 m 0 =0 / M 2 m 0 =1 ∼ t 3/z , along the critical line up to the LP. Finally, we explore all the critical exponents of the LP in detail, including the dynamic critical exponent θ that characterizes the initial slip of magnetization and the global persistence exponent θg associated to the probability P (t) that magnetization keeps its signal up to time t. Our estimates for the dynamic critical exponents at the Lifshitz point are z = 2.34(2) and θg = 0.336(4), values very different from the 3D Ising model (ANNNI model without the next-nearest-neighbor interactions at z-axis, i.e., J2 = 0) z ≈ 2.07 and θg ≈ 0.38. We also present estimates for the static critical exponents β and ν, obtained from extended time-dependent scaling relations. Our results for static exponents are in good agreement with previous works

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“…Moreover, this approach has proved to be efficient in determining the critical parameters of several models as shown in recent works (see for example the Refs. [14][15][16] ). In this paper, we present results from the study of the critical properties of the isotropic ferromagnetic twodimensional spin model with Z(5) symmetry, hereafter denoted as Z(5) model, by using time-dependent MC simulations.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium scaling explorations on a two-dimensionalZ(5)-symmetric model

Silva

Fernandes

Felício³

2014

Phys. Rev. E

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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. Besides, 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 FZ (Fateev-Zamolodchikov) point. Firstly, 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 of the 4-state Potts model (z ≈ 2.29).

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Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

Cited by 19 publications

References 38 publications

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

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

Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model

Nonequilibrium scaling explorations on a two-dimensionalZ(5)-symmetric model

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