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Journal of Experimental and Theoretical Physics

Critical dynamics of slightly disordered spin systems

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

Published Sep 1, 1998• 14 citations
Publisher

Abstract

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.

DOI
10.1134/1.558690

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Journal of Experimental and Theoretical Physics Letters•May 1, 2000•7 citations
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.
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.
The renormalization-group functions governing the critical behavior of the three-dimensional weakly-disordered Ising model are calculated in the five-loop approximation. The random fixed point location and critical exponents for impure Ising systems are estimated by means of the Padé-Borel-Leroy resummation of the renormalization-group expansions derived. The asymptotic critical exponents are found to be γ=1.325 ± 0.003, η=0.025 ± 0.01, ν= 0.671 ± 0.005, α=−0.0125 ± 0.008, β=0.344 ± 0.006, while for the correction-to-scaling exponent, a less accurate estimate ω=0.32 ± 0.06 is obtained.