Open AccessSemiclassical Approximation for the Curie – Weiss Model
Author(s) -
Aleksandr Bulekov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1740/1/012069
Subject(s) - semiclassical physics , tridiagonal matrix , mathematics , operator (biology) , subspace topology , spectrum (functional analysis) , marie curie , space (punctuation) , series (stratigraphy) , curie , mathematical analysis , coherent potential approximation , mathematical physics , curie temperature , quantum mechanics , physics , eigenvalues and eigenvectors , quantum , chemistry , computer science , repressor , european union , business , biology , economic policy , operating system , paleontology , biochemistry , transcription factor , electronic structure , gene , ferromagnetism
The paper is devoted to the construction of spectral series and the estimation of the approximation accuracy for the operator of the Curie – Weiss model. In the course of work, the operator is reduced to a tridiagonal form in the subspace of the original space, then to a second-order difference equation. The admissibility of reducing an operator to a subspace is presented. It is shown that the difference equation can be considered in the discrete semiclassical approximation. In the obtained classical system, the dependence of the turning points on the model parameters is investigated. The asymptotics of the spectrum of the Curie-Weiss operator is calculated and the accuracy of the approximation is estimated.