Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of the Solid State

Ising model of a dilute ferromagnet in the self-consistent field approximation

S. V. Semkin, Виктор Павлович Смагин

Published Jun 1, 2014• 5 citations
Publisher

Abstract

The method of averaging over the exchange interaction fields has been considered as applied to clusters of one and two magnetic atoms in the Ising model of a dilute ferromagnet, and a variant of fixed-scale group renormalization on the basis of this method has been constructed. It has been shown that the approximation obtained makes it possible to distinguish models with the site and bond dilutions.

DOI
10.1134/s1063783414060341

Related papers

Method of averaging over interaction fields for constructing the fixed-scale renormalization group transformation

S. V. Semkin, Виктор Павлович Смагин

The application of the method of averaging over exchange interaction fields to clusters consisting of two magnetic atoms in the Ising model using a simple lattice has been considered. A version of the fixed-scale renormalization group transformation has been constructed. The application of these methods to the square-lattice Ising magnet with anisotropic interaction has been discussed.

Physics of the Solid State•May 1, 2013•4 citations

Correlation functions of pure and diluted Ising magnets in the mean-field approximation

S. V. Semkin, Виктор Павлович Смагин

A mean-field method, which is a variant of the fixed-scale renormalization group transformation and is applied to both pure and diluted magnets, has been considered. It has been shown that, for pure magnets, the method is equivalent to the Bethe approximation. This method has been used to calculate the magnetization and correlation functions of both pure and bond-diluted Ising magnets.

Physics of the Solid State•Jul 1, 2014•1 citation

Critical properties of the site-diluted Ising ferromagnet

Julia M. Yeomans, Robin B. Stinchcombe

The site-diluted Ising ferromagnet is treated by a position space renormalisation group method. The method is briefly outlined and results obtained by considering three different two-dimensional clusters are presented. The results include the dependence of transition temperature T c on concentration p and the thermal exponents for the percolation and Ising fixed points. Corresponding results are also presented for the bond-diluted Ising ferromagnet.

Journal of Physics C Solid State Physics•Jul 14, 1978•28 citations

Mean Field Renormalization Group for Site‐Bond Diluted Ising Ferromagnets

C. Z. Yang, Z. Y. Li

Abstract It is shown that the mean field renormalization group techniques provide a reasonable description of the critical behaviour of the site‐bond diluted Ising model, both in the two‐dimensional system and the surface of a semi‐infinite three‐dimensional system.

physica status solidi (b)•Mar 1, 1988•12 citations

Averaging over interaction fields and spin correlations

S. V. Semkin, Victor Smagin

Averaging over interaction fields and spin correlations in the Ising modelIn the theory of phase transitions in magnetic systems, there are a small number of exact results.One of them is the well-known Onsager solution for the Ising model on a square lattice.The problem of phase transitions in magnets is a special case of the problem of many bodies.There are many approaches and methods in this area, including the method of averaging over exchange fields.The application of the distribution function over interaction fields to the study of the properties of a system of many interacting particles has been used for a long time.In previous works of the authors, the method of averaging over exchange fields was applied to the analysis of the magnetic properties of pure and diluted magnets.In this paper, we formulate and prove the relations on which the method of averaging over exchange fields can be based on clusters of several spins.It turns out that based only on the possibility of representing thermodynamic means as means of the distribution function of the fields, some nontrivial exact relations can be obtained.The paper considers the Ising model on simple lattices with coordination numbers of three and four.Exact expressions are found that connect the average products of three spins with spontaneous magnetization in the system.Inequalities are obtained that limit the limiting value of the Curie temperature and the maximum value of spontaneous magnetization at a given temperature.

Территория новых возможностей. Вестник Владивостокского государственного университета экономики и сервиса•Jan 1, 2020•0 citations

Использование усреднения по полям взаимодействия для построения приближенных методов в модели Изинга разбавленного магнетика

С.В. Сёмкин, В.П. Смагин, В.И. Люлько

Abstract The method of averaging over interaction fields has been analyzed as applied to the problems of statistical physics. This method has been theoretically justified as applied to a spin cluster. Based on the general relations obtained, approximate solutions for the bond-diluted Ising model are found. These approximate solutions are compared with the exact solution for a one-dimensional chain of bond-diluted Ising spins.

Physics of the Solid State•Jan 1, 2020•0 citations
The method of averaging over the exchange interaction fields has been considered as applied to clusters of one and two magnetic atoms in the Ising model of a dilute ferromagnet, and a variant of fixed-scale group renormalization on the basis of this method has been constructed. It has been shown that the approximation obtained makes it possible to distinguish models with the site and bond dilutions.
Averaging over interaction fields and spin correlations in the Ising modelIn the theory of phase transitions in magnetic systems, there are a small number of exact results.One of them is the well-known Onsager solution for the Ising model on a square lattice.The problem of phase transitions in magnets is a special case of the problem of many bodies.There are many approaches and methods in this area, including the method of averaging over exchange fields.The application of the distribution function over interaction fields to the study of the properties of a system of many interacting particles has been used for a long time.In previous works of the authors, the method of averaging over exchange fields was applied to the analysis of the magnetic properties of pure and diluted magnets.In this paper, we formulate and prove the relations on which the method of averaging over exchange fields can be based on clusters of several spins.It turns out that based only on the possibility of representing thermodynamic means as means of the distribution function of the fields, some nontrivial exact relations can be obtained.The paper considers the Ising model on simple lattices with coordination numbers of three and four.Exact expressions are found that connect the average products of three spins with spontaneous magnetization in the system.Inequalities are obtained that limit the limiting value of the Curie temperature and the maximum value of spontaneous magnetization at a given temperature.