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On constructive description of Gibbs measures for the Potts model on a Cayley tree

UDC 517.9 We consider the Potts model on a Cayley tree and prove the existence of Gibbs measures built by using the method suggested in [H. Akin, U. A. Rozikov, S. Temir, A new set of limiting Gibbs measures for the Ising model on a Cayley tree, J. Stat. Phys., 142, № 2, 314 – 321 (2011)]. In additi...

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Datum:2021
Hauptverfasser: Rahmatullaev, M., Rafikov , F. К., Azamov , Sh. Kh., Rahmatullaev, Muzaffar, Рахматуллаєв , M. M., Рафiков, Ф. К., Азамов, Ш. Х.
Format: Artikel
Sprache:Ukrainisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2021
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/6408
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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Zusammenfassung:UDC 517.9 We consider the Potts model on a Cayley tree and prove the existence of Gibbs measures built by using the method suggested in [H. Akin, U. A. Rozikov, S. Temir, A new set of limiting Gibbs measures for the Ising model on a Cayley tree, J. Stat. Phys., 142, № 2, 314 – 321 (2011)]. In addition, we prove that there exist $(k_0)$-translation invariant Gibbs measures for the Potts model on a Cayley tree and calculate the free energy of these Gibbs measures.
DOI:10.37863/umzh.v73i7.6408

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