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Russian Physics Journal

Computer simulation of the nonequilibrium critical behavior of disordered two-dimensional Ising systems

O. N. Markov, Vladimir V. Prudnikov

Published Aug 1, 1994• 0 citations
Publisher
DOI
10.1007/bf00559873

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Journal of Experimental and Theoretical Physics•Feb 1, 2020•3 citations
The simultaneous effect of nonequilibrium initial states and correlation between defects of the structure on the evolution of anisotropic disordered systems at the critical point has been analyzed. The field theory description of the nonequilibrium critical behavior of three-dimensional disordered systems with the longrange correlated defects has been given and the dynamical critical exponent of the short-time evolution has been calculated in the two-loop approximation without the use of the ɛ expansion. The values of the dynamical critical exponent obtained by using various methods for summing asymptotic series have been compared with the results of the computer simulation of the nonequilibrium critical behavior of the three-dimensional disordered Ising model in the short-time regime.
The influence of nonequilibrium initial states on the evolution of anisotropic systems with quenched uncorrelated structural defects at the critical point is studied. The field-theoretical description of the nonequilibrium critical behavior of 3D systems is obtained for the first time, and the dynamic critical exponent of the short-time evolution in the two-loop approximation without the use of ɛ expansion is calculated. The values of dynamic critical exponents calculated using the series resummation methods are compared with the results of computer simulation of nonequilibrium critical behavior of the 3D disordered Ising model in the short-time regime. It is demonstrated that the values of the critical exponents calculated in this paper are in better agreement with the results of computer simulation than the results of application of ɛ expansion.
Abstract The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.