Periodic Gibbs Measures and Their Extremality for the HC-Blume--Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree

N. M. Khatamov

Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 108-122.

Résumé

Periodic Gibbs measures for the HC-Blume–Capel model with a chemical potential with parameters $(\theta,\eta)$ on a Cayley tree in the case of a wand graph are studied. We prove that in this case for $\theta^3\leqslant\eta$ there exist precisely three periodic Gibbs measures, all of which are translation-invariant, while for $\theta^3>\eta$ there exist precisely three periodic Gibbs measures, one of which is translation-invariant and the other two are $2$-periodic (but not translation-invariant). The (non)extremality of these measures is also studied.

Détail

Keywords: Cayley tree, HC-Blume–Capel model, Gibbs measure, periodic measure, extremality of measures.
Mots-clés : configuration

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