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Semiclassical Approximation for the Curie-Weiss Model

Student: Bulekov Aleksandr

Supervisor: Evgeny Vybornyi

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Mathematical Methods of Modelling and Computer Technologies (Master)

Year of Graduation: 2020

Paper consists of 25 pages, contains 3 figures, 3 tables and refers to 4 sources. Key words: quantum Curie – Weiss model, difference equation, WKB method, turning points, operator spectrum. The object of study is quantum Curie – Weiss model. The aim of this work is to construct spectral series for Curie – Weiss model and to estimate accuracy of their approximation. In the course of the work, the operator of Curie – Weiss model reduced to a tridiagonal form. Then to a second order difference equation. The difference equation operator is considered in the discrete quasiclassical approximation. In the obtained classical system, the dependence of turning points on the model parameters is studied. The asymptotics of the spectrum of Curie – Weiss model is calculated and its asymptotic accuracy is estimated.

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