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Physics of the Solid State

Critical dynamics of disordered magnets in the three-loop approximation

Vladimir V. Prudnikov, С. В. Белим, E. V. Osintsev, Andrei A. Fedorenko

Published Aug 1, 1998• 9 citations
Publisher

Abstract

A field-theoretic description of the critical dynamics of magnetic systems with frozen nonmagnetic impurities is given. The values of the dynamical critical exponent in the three-loop approximation are obtained directly for three-dimensional systems using the Padé-Borel summation technique. A comparison is made with the values of the dynamical exponent for homogeneous systems calculated in the four-loop approximation as well as with the values obtained by Monte Carlo methods.

DOI
10.1134/1.1130564

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A field-theoretic description of the critical dynamics of magnetic systems with frozen nonmagnetic impurities is given. The values of the dynamical critical exponent in the three-loop approximation are obtained directly for three-dimensional systems using the Padé-Borel summation technique. A comparison is made with the values of the dynamical exponent for homogeneous systems calculated in the four-loop approximation as well as with the values obtained 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.
Abstract Within the field-theory approach, the critical behavior of disordered spin systems with frozen point impurities and additional dipole–dipole interactions is investigated. The system is described by the Heisenberg model. The computation is performed in a two-loop approximation in three-dimensional space. The Pade–Borel method is used to sum asymptotic series. It is shown that a threshold value of the dipole–dipole interaction intensity exists such that the influence of point frozen impurities becomes important once the value exceeds this threshold. For small values of the dipole–dipole interaction intensity, the dependence of critical exponents on it is obtained.
A field-theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations ~| x | - a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a 3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double , -expansion. The static and dynamic critical exponents 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.