This article is cited in 3 papers

Extremality of Gibbs Measures for the $HC$-Blume–Capel Model on the Cayley Tree

N. M. Khatamov

Tashkent, Uzbekistan

Abstract: In this paper, we consider translation-invariant Gibbs measures (TIGMs) for the $HC$-Blume–Capel model in case of “wands” with chemical potential with parameters $(\theta,\eta)$ on the Cayley tree. It is proved that, for $\eta\le\theta^{3}$, there is a unique TIGM and, for $\eta>\theta^{3}$, there are exactly three TIGMs in the case of “wands” with chemical potential for the model under consideration. In addition, the problem of the (non)extremality of these measures is studied.

Keywords: Cayley tree, configuration, $HC$-Blume–Capel model, Gibbs measure, translation-invariant measures, extremal measure.

UDC: 517.98

Received: 10.07.2021
Revised: 26.12.2021

DOI: 10.4213/mzm13217

 English version: Mathematical Notes, 2022, 111:5, 768–781

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