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Critical Dynamics of Three-Dimensional Spin Systems with Long-Range Interactions

С. В. Белим

Published Apr 9, 2005• 0 citations
OpenAlex

Abstract

A field-theoretic description of critical behavior of Ising systems with long-range interactions is obtained in the two-loop approximation directly in the three-dimensional space. It is shown that long-range interactions affect the relaxation time of the system.

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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.
Critical behavior of Ising ferromagnetic systems with the competition between short- and long-range interactions near the point of a second-order phase transition has been investigated. The effects of long-range interaction lead to the need to calculate the influence of next-nearest spins, which lie inside the sphere of a specific radius. The study was carried out for a power law of decreaseing the exchange integral with distance for a three-dimensional Ising model with a cubic lattice. A comparison with the results of a field-theoretical approach and data of real experiments has been carried out. It has been shown that the critical temperature grows linearly with an increase in the parameters of long-range interaction. Critical exponents have been calculated at different parameters of long-range interaction. It is shown that at small dimensions of a system it is the short-range interaction that exerts the dominant effect on the critical behavior of the system. With an increase in the linear dimension of the system, long-range forces begin to dominate.