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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 219, Number 3, Pages 597–609
DOI: https://doi.org/10.4213/tmf10669 (Mi tmf10669) 		 
Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree

M. M. Rahmatullaeva, B. M. Isakovb

a Romanovsky Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
b Andijan State University, Andizhan, Uzbekistan
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DOI: https://doi.org/10.4213/tmf10669
Abstract: We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model.
Keywords: Cayley tree, configuration, Ising–Potts model, Gibbs measure, translation-invariant Gibbs measure.
Received: 25.12.2023
Revised: 02.02.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 219, Issue 3, Pages 1048–1059
DOI: https://doi.org/10.1134/S0040577924060114
Bibliographic databases:
Document Type: Article
MSC: 60K35,82B26
Language: Russian
Citation: M. M. Rahmatullaev, B. M. Isakov, “Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree”, TMF, 219:3 (2024), 597–609; Theoret. and Math. Phys., 219:3 (2024), 1048–1059
Citation in format AMSBIB
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\by M.~M.~Rahmatullaev, B.~M.~Isakov
\paper Translation-invariant Gibbs measures for the~Ising--Potts model on a~second-order Cayley tree
\jour TMF
\yr 2024
\vol 219
\issue 3
\pages 597--609
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\crossref{https://doi.org/10.4213/tmf10669}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4767973}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...219.1048R}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 219
\issue 3
\pages 1048--1059
\crossref{https://doi.org/10.1134/S0040577924060114}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85196800377}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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