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

N. M. Khatamov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 256-277

Résumé

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.

Détail

Keywords: Cayley tree, Blume–Capel HC-model, Gibbs measure, translation-invariant measures, extreme measure.
Mots-clés : configuration

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