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Journal of Experimental and Theoretical Physics Letters

Critical dynamics of spin systems in the four-loop approximation

Vladimir V. Prudnikov, A. V. Ivanov, Andrei A. Fedorenko

Published Dec 1, 1997• 34 citations
Publisher

Abstract

A field-theoretic description of the critical dynamics of spin systems is constructed. Using the Padé-Borel summation technique, the dynamic critical exponent for two-and three-dimensional systems is evaluated directly in the four-loop approximation. The results are compared with the values obtained for the dynamic exponent by Monte Carlo methods.

DOI
10.1134/1.567606

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Theoretical and Mathematical Physics•Mar 1, 2017•1 citation
A field-theoretic description of the critical dynamics of spin systems is constructed. Using the Padé-Borel summation technique, the dynamic critical exponent for two-and three-dimensional systems is evaluated directly in the four-loop approximation. The results are compared with the values obtained for the dynamic exponent by Monte Carlo methods.
This paper is a field theoretic description of the critical dynamics of spin systems with frozen nonmagnetic impurities. For three-dimensional systems the dynamical critical exponent is found directly by employing the three-loop approximation with the Padé-Borel summation technique. The results are compared with those obtained by calculating the dynamical exponent for homogeneous systems in the four-loop approximation, and with the values obtained by computer simulation of the critical dynamics by Monte Carlo methods. Calculations of the dynamical exponent for the two-dimensional Ising model in the four-loop approximation are also presented.
A field-theoretic description of phase transformations in complex systems with two interacting order parameters is given. For three-dimensional systems in the two-loop approximation a renormalization-group analysis of the scaling functions is carried out directly, and the fixed points corresponding to stability of the bicritical and tetracritical behavior are identified. The critical exponents at the multicritical points in the two-loop approximation are calculated with the use of the Padé-Borel summation technique.
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.
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.