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Journal of Physics Conference Series

Non-equilibrium critical behavior of the 3D classical Heisenberg model

Evgenii A. Pospelov, Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Лях Анастасия Сергеевна

Published Feb 1, 2019• 8 citations
Publisher

Abstract

We have investigated the non-equilibrium critical behavior of the three-dimensional classical Heisenberg model with evolution from various initial states. Initial states with magnetization m 0 ≠ 0 lead to a new time scale with the exponent k > 0 which produces complex universal scaling forms on the temporal behavior of the magnetization, the autocorrelation function, and the response function. Aging effects have been revealed in two-time behavior of the autocorrelation function with evolution from various initial states. We show that the slowing down of the autocorrelation function during the evolution from high-temperature initial state is considerably more slow than for case of the evolution from low-temperature initial state. Using scaling forms of the magnetization and the autocorrelation function, the values of critical exponents z = 2.035(4), θ ' = 0.490(1), and k = 1/( θ ' + β / νz ) = 1.340(4) were calculated.

DOI
10.1088/1742-6596/1163/1/012020

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We have investigated the non-equilibrium critical behavior of the three-dimensional classical Heisenberg model with evolution from various initial states. Initial states with magnetization m 0 ≠ 0 lead to a new time scale with the exponent k > 0 which produces complex universal scaling forms on the temporal behavior of the magnetization, the autocorrelation function, and the response function. Aging effects have been revealed in two-time behavior of the autocorrelation function with evolution from various initial states. We show that the slowing down of the autocorrelation function during the evolution from high-temperature initial state is considerably more slow than for case of the evolution from low-temperature initial state. Using scaling forms of the magnetization and the autocorrelation function, the values of critical exponents z = 2.035(4), θ ' = 0.490(1), and k = 1/( θ ' + β / νz ) = 1.340(4) were calculated.
The dynamic critical behaviour of the three-dimensional classical Heisenberg model was studied by using short-time Monte Carlo simulations. The dynamic critical exponents z , θ and θ g , as well as the static critical exponents ν and β, were estimated by following the time evolution of the z -component of the total magnetization and its moments of higher order. The anomalous dimension of the magnetization x 0 was also calculated from a relation obtained through finite size scaling in the non-equilibrium stage. Afterwards, the local persistence exponent θ l was obtained by following the power law behaviour of the local persistence probability when the system was quenched from high temperatures to the null one ( T = 0). The time evolution of P l ( t ) was also analysed for T >0 and the expected exponential stretch was observed.
Abstract Monte Carlo study of non-equilibrium critical behavior of three-dimensional Heisenberg model in isotropic case and with anisotropy of easy axis type is carried out. Relaxational Glauber-like dynamics of these models with evolution from high-temperature initial state is investigated. Realization of aging is demonstrated for two-time dependence of the autocorrelation function and dynamical susceptibility. Asymptotic fluctuation-dissipation ratios are determined for isotropic X ∞ = 0.383(6) and anisotropic X ∞ = 0.392(7) Heisenberg models. Significant influence of easy-axis anisotropy on non-equilibrium critical behavior of the 3D Heisenberg model leading to characteristics typical for the 3D Ising model is revealed.
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.
A numerical Monte Carlo study of different initial states, magnetic anisotropy of “easy axis” type, and structural defects influence on non-equilibrium critical behavior of the classical three-dimensional Heisenberg model has been carried out. Analysis of time dependence of the magnetization and the autocorrelation function for isotropic Heisenberg model has shown strong influence of initial states on relaxation of the magnetization and aging effects in behavior of the autocorrelation function, which are characterized by anomalous slowing down of relaxation and correlation in system with increasing waiting time. Study of the anisotropic Heisenberg model with magnetic anisotropy of “easy axis” type has revealed that behavior of the magnetization and autocorrelation function in long-time regime is characterized by critical exponents of the three-dimensional Ising model and more fast decay of the autocorrelation function than for isotropic Heisenberg model. It has been revealed that in structurally disordered isotropic Heisenberg model relaxing from the low-temperature initial state, the significant changes of non-equilibrium aging phenomena in comparison with pure model are observed due to the pinning of domain walls on defects. It has been shown that during this relaxation process a strong slowing-down of time dependence of the autocorrelation function is realized. As a result, superaging effects occur in long-term behavior of the autocorrelation function with values of the superaging exponent μ=2.6(1). During evolution of system from high-temperature initial state, the presence of structural defects leads to increase of aging effects in aging regime, but their influence is found irrelevant in long-time regime.
The effect of various initial magnetizations m0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m0 These subclasses correspond to the system evolution from the high-temperature (m0 = 0) and low-temperature (m0 = 1) initial states with limit FDRs characteristic of these states.
We numerically investigate the stationary and nonequilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the nonconserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin-exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization-group prediction: While the critical aging collapse exponent assumes a universal value, the associated temporal decay exponent in the two-time spin autocorrelation function depends on the initial distribution of the conserved fields; here, specifically on the width of the initial spin orientation distribution.