Nonequilibrium scaling explorations on a 2D Z(5)-symmetric model

Abstract

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 $\beta /\nu z$ 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 $\beta$ and 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 $z\approx 2.28$ very close of the 4-state Potts model ($z\approx 2.29$).

arXiv comment11 pages, 7 figures

References in corpus (10)

• Generalized Dynamic Scaling for Critical Magnetic Systems
• Dynamic Monte Carlo Measurement of Critical Exponents
• Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics
• Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation
• Dynamic Approach to Weak First Order Phase Transitions
• Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems
• Novel considerations about the non-equilibrium regime of the tricritical point in a metamagnetic model: localization and tricritical exponents
• An alternative order parameter for the 4-state Potts model
• Critical dynamics of the Potts model: short-time Monte Carlo simulations
• Time-dependent Monte Carlo simulations of the critical and Lifshitz points of the ANNNI model

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• Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion
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• Short-time dynamics in phase-ordering kinetics