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

TL;DR

This study explores the dynamic critical behavior of the 2D Z(5)-symmetric spin model using short-time Monte Carlo simulations, identifying critical points, phase transitions, and critical exponents, including at the special FZ point.

Contribution

It provides new estimates of critical points, phase transition types, and critical exponents for the 2D Z(5) model, especially at the FZ point, using out-of-equilibrium simulations.

Findings

Critical points and phase transition types identified.

Static critical exponents match exact results.

Dynamic critical exponent z ≈ 2.28 close to 4-state Potts 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 $% \nu $ 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 ($z\approx 2.29$).