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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 2, Pages 256–277
DOI: https://doi.org/10.35634/vm220207
(Mi vuu810)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Extremality of some Gibbs measures for the Blume-Capel HC-model on a Cayley tree

N. M. Khatamovab

a Namangan State University, ul. Uychi, 316, Namangan, 160119, Uzbekistan
b Institute of Mathematics named after V.I. Romanovsky, ul. Universitetskaya, 9, Tashkent, 100174, Uzbekistan
Full-text PDF (389 kB) Citations (1)
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Abstract: In this paper, we consider translation-invariant Gibbs measures (TIGM) for the Blume–Capel HC-model in the case of a “generalized wand” on a second-order Cayley tree. An approximate critical value of $\theta_{cr}$ is found such that for $\theta \geq\theta_{cr}$ there is only one TIGM, and for $0<\theta<\theta_{cr}$ there are exactly three TIGMs in the case of “generalized wand” for the model under consideration. In addition, the (non)extreme problem for these measures is studied.
Keywords: Cayley tree, configuration, Blume–Capel HC-model, Gibbs measure, translation-invariant measures, extreme measure.
Received: 19.04.2022
Accepted: 28.05.2022
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 82B05, 82B20, 60K35
Language: Russian
Citation: N. M. Khatamov, “Extremality of some Gibbs measures for the Blume-Capel HC-model on a Cayley tree”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022), 256–277
Citation in format AMSBIB
\Bibitem{Kha22}
\by N.~M.~Khatamov
\paper Extremality of some Gibbs measures for the Blume-Capel HC-model on a Cayley tree
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 2
\pages 256--277
\mathnet{http://mi.mathnet.ru/vuu810}
\crossref{https://doi.org/10.35634/vm220207}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4456919}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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