Effect of the Initial States, the Anisotropy, and Structural Defects on a Nonequilibrium Critical Behavior of the Three-Dimensional Heisenberg Model

Abstract

A numerical Monte Carlo study has been performed on the influence of various initial states, easy-axis-type magnetic anisotropy, and structural defects on a nonequilibrium critical behavior of the classical three-dimensional Heisenberg model. An analysis of the time dependence of the magnetization and the autocorrelation function for the isotropic Heisenberg model shows substantial influence of the initial states on the relaxation of the magnetization and the aging effects in the behavior of the autocorrelation function, which are characterized by anomalous slowing down of the relaxation and correlation in the system as the waiting time increases. The study of the anisotropic Heisenberg model shows that the behavior of the magnetization and the autocorrelation function in a long-time regime is characterized by the critical exponents of the three-dimensional Ising model with a faster time decay of the autocorrelation function than that for the isotropic model. It has been revealed that the existence of structural defects in the case of the evolution of the system from the low-temperature initial state leads to an anomalously significant slowing down of the autocorrelation function. These features in the behavior of the autocorrelation function are characterized by the “superaging” effect with “superaging” exponent μ = 2.6(1) and related to the pinning of domain walls on structural defects during a nonequilibrium change in the domain structure of the system. In the case of evolution from the high-temperature initial state, the structural defects enhance the aging effect in the aging regime but their influence is irrelevant in the long-time regime.