Geodesic
Extremality of Gibbs Measures for the $HC$-Blume--Capel Model on the Cayley Tree
Matematičeskie zametki, Tome 111 (2022) no. 5, pp. 762-777

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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, $HC$-Blume–Capel model, Gibbs measure, translation-invariant measures, extremal measure.
Mots-clés : configuration 
@article{MZM_2022_111_5_a9,
     author = {N. M. Khatamov},
     title = {Extremality of {Gibbs} {Measures} for the $HC${-Blume--Capel} {Model} on the {Cayley} {Tree}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {762--777},
     publisher = {mathdoc},
     volume = {111},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_5_a9/}
}
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N. M. Khatamov. Extremality of Gibbs Measures for the $HC$-Blume--Capel Model on the Cayley Tree. Matematičeskie zametki, Tome 111 (2022) no. 5, pp. 762-777. http://geodesic.mathdoc.fr/item/MZM_2022_111_5_a9/