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Moscow University Physics Bulletin

The Critical Behavior of Disordered Systems with Dipole–Dipole Interactions

С. В. Белим

Published Jul 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.3103/s0027134920040049

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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.
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-theoretical description of the behavior of a disordered Ising system with long-range interactions is presented. The description is performed in the two-loop approximation in three dimensions using the Padé-Borel resummation technique. The renormalization group equations are analyzed, and the fixed points determining the critical behavior of the system are found. It is shown that the effect of frozen structural defects on a system with long-range interactions may cause a change in its critical behavior or smearing of the phase transition.
A field-theoretical description of the behavior of a disordered Ising system with long-range interaction is presented. The description is performed in the two-loop approximation in three dimensions using the Pade-Borel resummation technique. The renormalization group equations are analyzed, and the fixed points determining the critical behavior of the system are found. It is shown that the effect of frozen structural defects on a system with long-range interaction may cause a change in its critical behavior or smearing of the phase transition.
We analyze the critical behavior of isotropic systems with dipole-dipole interaction by renormalization-group methods in fixed space-time dimensions. Working in three-dimensional theory we analytically find three-loop expressions for critical exponents in the limit of dominating dipole-dipole forces. Resummation of the series obtained provides numerical values close to O(3)-theory predictions, justifying the applicability of such a simplified model to systems with strong dipole-dipole interaction.
A field-theoretic description of the critical behavior of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of a model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For the case with 1-step RSB the fixed points (FP's) corresponding to stability of the various types of critical behavior are identified with the use of the Pade-Borel summation technique. Analysis of FP's has shown a stability of the critical behavior of the weakly disordered systems with respect to RSB effects and realization of a former scenario of disorder influence on critical behavior.