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Physica A Statistical Mechanics and its Applications

Non-equilibrium critical relaxation of the three-dimensional Ising model

Nobuyasu Ito

Published Feb 1, 1993• 107 citations
Publisher
DOI
10.1016/0378-4371(93)90111-g

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From the non-equilibrium critical relaxation study of the two-dimensional Ising model, the dynamical critical exponent z is estimated to be 2.165 ± 0.010 for this model. The relaxation in the ordered phase of this model is consistent with exp (−√t/τ) behavior. The interface energy of the three-dimensional Ising model is studied and the critical exponent of the correlation length ν and the critical amplitude of the surface tension σ0 are estimated to be 0.6250 ± 0.0025 and 1.42 ± 0.04, respectively. A dynamic Monte Carlo renormalization group method is successfully applied to the equilibrium properties of the three-dimensional Ising model.
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.