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arXiv:cond-mat/0502173 · Journal of Experimental and Theoretical Physics

Effects of long-range interaction on critical and multicritical behavior of compressible disordered systems

С. В. Белим

Published May 1, 2005• 0 citations
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Abstract

A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a . A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.

DOI
10.1134/1.1947318

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A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a . A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.
A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to critical and tricritical behavior of the systems are determined. Elastic deformations are shown to changes in critical and tricritical behavior of disordered compressible systems with long-range interactions. The critical exponents characterizing a system in the critical and tricritical regions are determined.
A field-theoretic approach is applied to describe behavior of homogeneous three-dimensional systems with long-range interactions defined by two order parameters at bicritical and tetracritical points. Renormalization-group equations are analyzed in the two-loop approximation by using the Padé-Borel summation technique. The fixed points corresponding to various types of multicritical behavior are determined. It is shown that effects due to long-range interactions can be responsible for a change from bicritical to tetracritical behavior.
A field-theoretical description of the behavior of compressible Ising systems with long-range interactions is presented. The description is performed in the two-loop approximation in three dimensions with the use of the Padé-Borel resummation technique. The renormalization group equations are analyzed, and the fixed points that determine the critical behavior of the system are found. It is shown that the effect of elastic deformations on a system with a long-range interaction causes changes in its critical, as well as multicritical, behavior.
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.