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Theoretical and Mathematical Physics

Renormalization group description of the nonequilibrium critical dynamics of spin systems at the fixed space dimension d = 3

I. V. Lavrukhin, Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov

Published Mar 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s0040577917030096

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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.
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 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 theoretic renormalization-group approach is applied to the study of short-time critical behavior of the ddd-dimensional spin systems (model A) in the presence of quenched impurities with a long-range correlations decaying as ${r}^{\ensuremath{-}(d\ensuremath{-}\ensuremath{\rho})}$. The asymptotic scaling laws are studied in the frame of a double expansion in $ϵ=4\ensuremath{-}d$ and $\ensuremath{\rho}$ with $\ensuremath{\rho}$ of order ϵϵϵ. In d<4d<4d<4, the initial slip exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ of the magnetization and $\ensuremath{\theta}$ of the response function, are calculated up to two-loop order. The crossover between fixed points is obtained. The long-time limit of the fluctuation-dissipation ratio is found in the aging regime, and its connection to equilibrium quantities is discussed. The comparison of our results with those of other systems without long-range correlated quenched impurities is also investigated.
The effect of various initial magnetizations m0 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 m0 These subclasses correspond to the system evolution from the high-temperature (m0 = 0) and low-temperature (m0 = 1) initial states with limit FDRs characteristic of these states.