Nonequilibrium scaling explorations on a two-dimensionalZ(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 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).

Affinities and disagreements between Mean-field and short-range critical dynamics

“…with ϑ = 1 νz which is valid when δ << 1, and finally with ν and z in hands, we return to 3 and calculate β. These three power laws can be used to determine β, ν and z for the critical (see for example [8]) and tricritical [4,5] in both two and three-dimensional nonequilibrium simulations which is known as short-time dynamics, but the question is: could they be observed in mean-field regime? Moreover, how works the initial anomalous behavior of the magnetization for m 0 << 1?…”

“…In this paper, we will show the peculiarities of the nonequilibrium critical dynamics of mean-field Ising-like systems for both: spin 1/2 (Ising) and spin 1 (BC). We will localize the critical temperature with a method previously used for systems with SR interactions [9] but that we here show to be properly interesting to estimate the critical parameters in MF systems. After that, we show that there is a notorious difference between the relaxation of the nonequilibrium critical dynamics from disordered initial systems for two-dimensional and MF systems, via MC simulations and some analytical results.…”

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

“…The critical bifurcation point at nonzero temperature (see Fig. 1) is inferred to be the Fateev-Zamolodchikov point [64], where the first-order and BKT transition lines terminate [65][66][67]. For further clarification of the peculiarity of the critical phase, let us consider the effects of the spin degrees of freedom by comparing the above results with those for the model without spin degrees of freedom.…”

First numerical evidence of Janssen-Oerding's prediction in a three-dimensional spin model far from equilibrium

“…Zheng and many collaborators (for a review, see [3]) numerically explored such scaling relation via MC simulations under many aspects. In the sequence, many other authors enriched the method by proposing new amounts, refinements, and other models, including also that ones without defined Hamiltonian, and even models with longrange interaction (see, for example [4][5][6][7][8][9][10]).…”

“…The computation of critical exponents along the critical line captures the crossover effects at proximities of the tricritical point. We start our study by computing the coefficient of determination that here measures the "quality" of powerlaw [15]:…”