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Journal of Experimental and Theoretical Physics

Nonequilibrium critical relaxation of structurally disordered systems in the short-time regime: Renormalization group description and computer simulation

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Ivan A. Kalashnikov, М. В. Рычков

Published Feb 1, 2010• 11 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776110020093

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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.
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 values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ of the short time evolution of a system with an n -component order parameter is calculated within a dynamical dissipative model using the method of Σ-expansion in a three-loop approximation. Numerical values of θ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.
The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.
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.
We study nonequilibrium critical relaxation properties of systems with quenched extended defects, correlated in ${\ensuremath{\varepsilon}}_{d}$ dimensions and randomly distributed in the remaining $d\ensuremath{-}{\ensuremath{\varepsilon}}_{d}$ dimensions. Using a field-theoretic renormalization-group approach, we find the scaling behavior of the nonequilibrium response and correlation functions and calculate the initial slip exponents $\ensuremath{\theta}$ and ${\ensuremath{\theta}}^{\ensuremath{'}},$ which describe the growth of correlations during the initial stage of the critical relaxation, in the two-loop approximation.