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arXiv:1005.5218 · Physical Review E

Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Aleksandr Krinitsyn, Andrey N. Vakilov, Evgenii A. Pospelov, М. В. Рычков

Published Jan 26, 2010• 44 citations
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Abstract

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

DOI
10.1103/physreve.81.011130

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Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.
Using Monte Carlo simulations it was studied the non-equilibrium critical evolution in the three-dimensional site-diluted weakly and strongly disordered Ising model with spin concentrations p=0.80 and 0.60. The values of exponents for power-law time dependence of magnetization and the autocorrelation function were determined. The values of two independent dynamic critical exponents z and θ were calculated. They demonstrate a good agreement with results of theoretical-field description and results of experimental investigations for weakly diluted Ising-like systems, but show visible differences with values of these exponents for strongly disordered Ising systems.
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.
We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the ± J Ising model along the paramagnetic–ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size dependence of suitably defined autocorrelation times at the critical point provides the estimate z = 2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from to T c . In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behaviour gives an estimate of z that is perfectly consistent with the equilibrium estimate z = 2.35(2).
Critical short-time dynamics in a bond-diluted Ising model is investigated in this paper using numerical simulations. The effective static and dynamic critical exponents determined by the power-law scaling are found to depend strongly on bond concentration and initial state. For weak disorder, the short-time scaling relations for the system quenched from high temperature are observed to hold. In the strong dilution limit, multiscaling relations for the system starting from the ordered state are found. Corrections to the short-time scaling are proposed. The effect of disorder on critical short-time dynamics is discussed.