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

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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.
Keywords: Cayley tree, HC-Blume–Capel model, Gibbs measure, periodic measure, extremality of measures.
Mots-clés : configuration 
@article{MZM_2024_115_1_a7,
     author = {N. M. Khatamov},
     title = {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}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {108--122},
     publisher = {mathdoc},
     volume = {115},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_1_a7/}
}
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N. M. Khatamov. 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. Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 108-122. http://geodesic.mathdoc.fr/item/MZM_2024_115_1_a7/