Abstract:
We study fertile hard-core models with three states and an activity parameter λ>0 on the Cayley tree of order k=3. It is known that there are four types of such models. For two of them, we find the regions where the unique translation-invariant Gibbs measure is (not) extremal. For one of the considered models, we find the conditions under which the extremal measure is not unique.
Citation:
R. M. Khakimov, K. O. Umirzakova, “Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order k=3”, TMF, 206:1 (2021), 112–124; Theoret. and Math. Phys., 206:1 (2021), 97–108
\Bibitem{KhaUmi21}
\by R.~M.~Khakimov, K.~O.~Umirzakova
\paper Extremality of the~unique translation-invariant Gibbs measure for hard-core models on the~Cayley tree of order $k=3$
\jour TMF
\yr 2021
\vol 206
\issue 1
\pages 112--124
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\crossref{https://doi.org/10.4213/tmf9965}
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\jour Theoret. and Math. Phys.
\yr 2021
\vol 206
\issue 1
\pages 97--108
\crossref{https://doi.org/10.1134/S0040577921010062}
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Linking options:
https://www.mathnet.ru/eng/tmf9965
https://doi.org/10.4213/tmf9965
https://www.mathnet.ru/eng/tmf/v206/i1/p112
This publication is cited in the following 4 articles:
B. Z. Tozhiboev, R. M. Khakimov, “Mery Gibbsa dlya HC-modeli v sluchae grafa tipa “klyuch” na dereve Keli”, Matem. zametki, 117:4 (2025), 575–590
R. M. Khakimov, B. Z. Tozhiboev, “Gibbs measures for fertile models with hard-core interactions
and four states”, Theoret. and Math. Phys., 219:2 (2024), 823–838
Rustamjon Khakimov, Muhtorjon Makhammadaliev, Kamola Umirzakova, “Alternative Gibbs measure for fertile three-state Hard-Core models on a Cayley tree”, Phase Transitions, 2024, 1
F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the λ-model on the binary Cayley tree”, Theoret. and Math. Phys., 210:3 (2022), 411–424