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Article

Semiclassical Approximation for the Curie – Weiss Model

Булеков А. А.

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 secondorder 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.