КРИТИЧНА ПОВЕДІНКА СТРУКТУРНО-НЕВПОРЯДКОВАНИХ СИСТЕМ З ДАЛЕКОСЯЖНОЮ ВЗАЄМОДІЄЮ. (Ukrainian)

CRITICAL BEHAVIOR OF STRUCTURALLY DISORDERED SYSTEMS WITH LONG-RANGE INTERACTION. (English)

Some physical systems, although different by their microscopic nature, in the vicinity of critical points can have similar thermodynamic and structural properties governed by universal power laws. Such systems are grouped into the so-called universality classes. The latter are determined by such global characteristics as the type of interaction, space dimensionality, symmetry, and the number of components of the order parameter. Therefore, it is interesting to investigate how the mutual influence of these characteristics can affect the critical features of the system. The goal of our research is to analyze the changes in the critical behavior of a many-particle magnetic system under the influence of two competing factors: long-range interaction and weak structural disorder. Using the example of an n-vector model in a d-dimensional space, we will investigate ferromagnetic ordering in a structurally disordered magnet with the long-range interaction decaying with the distance x as J(x)~x^-d-σ, with the control parameter σ. The analysis is carried out using the field-theoretical renormalization group methods, which makes it possible to identify the universality classes of the system under consideration, their change with global parameters, and to determine the universal characteristics of critical behavior (critical exponents and marginal dimensions). It will be shown that there exists such a region of parameters (d,n,σ), where the long-range interaction and structural disorder lead to a synergistic effect and the appearance of a new, “random long-range” universality class. We obtain the renormalization group functions in the three-loop approximation, and calculate the correlation length critical exponent ν(ϵ',n) as a perturbation theory series in ϵ′ = 2σ − d. Quantitative estimates are obtained using asymptotic series resummation methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Physical Studies is the property of Journal of Physical Studies and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)