Geodesic
Extremality of some Gibbs measures for the Blume-Capel HC-model on a Cayley tree
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 256-277

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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.
Keywords: Cayley tree, Blume–Capel HC-model, Gibbs measure, translation-invariant measures, extreme measure.
Mots-clés : configuration 
@article{VUU_2022_32_2_a6,
     author = {N. M. Khatamov},
     title = {Extremality of some {Gibbs} measures for the {Blume-Capel} {HC-model} on a {Cayley} tree},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {256--277},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a6/}
}
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N. M. Khatamov. Extremality of some Gibbs measures for the Blume-Capel HC-model on a Cayley tree. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 256-277. http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a6/