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Herald of Omsk University Series Psychology

Ренормгрупповое исследование неравновесной критической динамики. Расчет флуктуационно-диссипативного отношения в двухпетлевом приближении

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Д. Н. Куликов, I. V. Lavrukhin

Published Jan 1, 2015• 0 citations
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Abstract

Renormalization method is applied to relaxation dynamics of non-equilibrium Model A quenched to the critical point from high-temperature initial state. Violations of Fluctuation-Dissipation Theorem and two-time dependences of response and correlation functions are investigated. Universal Fluctuation-Dissipation Ratio is computed up to the second-loop order at the fixed spatial dimension d = 3. The summation Pade – Borel method is applied for calculation of limit Fluctuation-Dissipation Ratio.

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We present the method and results of a renormalization group description of nonequilibrium critical relaxation of model A with evolution from an initial high-temperature state. We calculate the two-time dependence of the correlation function and response function and find a violation of the fluctuationdissipation theorem in the nonequilibrium critical regime. For the limit fluctuation-dissipation relation, which is a universal property of the nonequilibrium critical dynamics, we calculate the fluctuation and impurity corrections in the two-loop approximation at the fixed space dimension d = 3 using Padé–Borel summation for asymptotic series.

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Non-equilibrium critical dynamics

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We now begin our exposition of universal dynamic scaling behavior that emerges under non-equilibrium conditions. We are mainly concerned with the relaxational models A and B here, but also touch on other dynamic universality classes. First, we consider non-equilibrium critical relaxation from a disordered initial state, and compute the associated universal scaling exponents within the dynamic renormalization group framework. Related phenomena in the early-time regime, prior to reaching temporally translationally invariant asymptotics, are ‘aging’ and a non-equilibrium fluctuation-dissipation ratio, both of which have enjoyed prominence in the literature on ‘glassy’ kinetics. In this context, we derive the critical initial slip exponent for the order parameter, and briefly discuss interesting persistence properties. Second, we explore the long-time scaling laws in phase ordering kinetics and coarsening for the relaxational models, following a fast temperature ‘quench’ into the ordered phase, in systems with either non-conserved or conserved order parameters. Aside from a few explicit computations in the spherical model limit (wherein the number of order parameter components n → ∞), we largely employ phenomenological considerations and scaling theory, stressing the importance of topological defects for energy dissipation during coarsening. Next we address the question how violations of Einstein's relation that links relaxation coefficients and noise correlations might affect the asymptotic dynamic critical scaling behavior. Whereas in systems with non-conserved order parameter typically the equilibrium scaling laws are recovered in the vicinity of the critical point, in contrast genuinely novel universality classes may emerge in the case of a conserved parameter, provided it is driven out of equilibrium in a spatially anisotropic fashion.

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Using Monte Carlo simulations it was studied the non-equilibrium critical relaxation in the three-dimensional site-diluted Ising model with spin concentration p=0.80. The values of exponents for power-law time dependence of magnetization and Binder cumulant were determined with the use of corrections to scaling method. The dynamic critical exponent z, the ratio of static exponents p7v and exponent of correction to scaling со were calculated. They demonstrate a good agreement with results of theoretical-field description and results of experimental investigations for diluted Ising-like systems.

Herald of Omsk University Series Psychology•Jan 1, 2007•0 citations
Renormalization method is applied to relaxation dynamics of non-equilibrium Model A quenched to the critical point from high-temperature initial state. Violations of Fluctuation-Dissipation Theorem and two-time dependences of response and correlation functions are investigated. Universal Fluctuation-Dissipation Ratio is computed up to the second-loop order at the fixed spatial dimension d = 3. The summation Pade – Borel method is applied for calculation of limit Fluctuation-Dissipation Ratio.
AbstractThe effect of various initial magnetizations m _0 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 m _0 These subclasses correspond to the system evolution from the high-temperature ( m _0 = 0) and low-temperature ( m _0 = 1) initial states with limit FDRs characteristic of these states.
We present the method and results of a renormalization group description of nonequilibrium critical relaxation of model A with evolution from an initial high-temperature state. We calculate the two-time dependence of the correlation function and response function and find a violation of the fluctuationdissipation theorem in the nonequilibrium critical regime. For the limit fluctuation-dissipation relation, which is a universal property of the nonequilibrium critical dynamics, we calculate the fluctuation and impurity corrections in the two-loop approximation at the fixed space dimension d = 3 using Padé–Borel summation for asymptotic series.
We now begin our exposition of universal dynamic scaling behavior that emerges under non-equilibrium conditions. We are mainly concerned with the relaxational models A and B here, but also touch on other dynamic universality classes. First, we consider non-equilibrium critical relaxation from a disordered initial state, and compute the associated universal scaling exponents within the dynamic renormalization group framework. Related phenomena in the early-time regime, prior to reaching temporally translationally invariant asymptotics, are ‘aging’ and a non-equilibrium fluctuation-dissipation ratio, both of which have enjoyed prominence in the literature on ‘glassy’ kinetics. In this context, we derive the critical initial slip exponent for the order parameter, and briefly discuss interesting persistence properties. Second, we explore the long-time scaling laws in phase ordering kinetics and coarsening for the relaxational models, following a fast temperature ‘quench’ into the ordered phase, in systems with either non-conserved or conserved order parameters. Aside from a few explicit computations in the spherical model limit (wherein the number of order parameter components n → ∞), we largely employ phenomenological considerations and scaling theory, stressing the importance of topological defects for energy dissipation during coarsening. Next we address the question how violations of Einstein's relation that links relaxation coefficients and noise correlations might affect the asymptotic dynamic critical scaling behavior. Whereas in systems with non-conserved order parameter typically the equilibrium scaling laws are recovered in the vicinity of the critical point, in contrast genuinely novel universality classes may emerge in the case of a conserved parameter, provided it is driven out of equilibrium in a spatially anisotropic fashion.
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.
Using Monte Carlo simulations it was studied the non-equilibrium critical relaxation in the three-dimensional site-diluted Ising model with spin concentration p=0.80. The values of exponents for power-law time dependence of magnetization and Binder cumulant were determined with the use of corrections to scaling method. The dynamic critical exponent z, the ratio of static exponents p7v and exponent of correction to scaling со were calculated. They demonstrate a good agreement with results of theoretical-field description and results of experimental investigations for diluted Ising-like systems.