Section
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Mathematics
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Title
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Extremality of some Gibbs measures for the Blume–Capel HC-model on a Cayley tree
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Author(-s)
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Khatamov N.M.ab
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Affiliations
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Institute of Mathematics, National Academy of Sciences of Uzbekistana,
Namangan State Universityb
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Abstract
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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.
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Keywords
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Cayley tree, configuration, Blume–Capel HC-model, Gibbs measure, translation-invariant measures, extreme measure
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UDC
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517.98
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MSC
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82B05, 82B20, 60K35
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DOI
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10.35634/vm220207
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Received
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19 April 2022
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Language
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Russian
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Citation
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Khatamov N.M. Extremality of some Gibbs measures for the Blume–Capel HC-model on a Cayley tree, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 2, pp. 256-277.
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