|
This article is cited in 3 scientific papers (total in 3 papers)
Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order $k=3$
R. M. Khakimova, K. O. Umirzakovab a Namangan Department, Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Namangan, Uzbekistan
b Namangam State University, , Namangan, Uzbekistan
Abstract:
We study fertile hard-core models with three states and an activity parameter $\lambda>0$ 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.
Keywords:
Cayley tree, configuration, hard-core model, fertile graph, Gibbs measure, translation-invariant measure, measure extremality.
Received: 03.08.2020 Revised: 03.08.2020
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
Linking options:
https://www.mathnet.ru/eng/tmf9965https://doi.org/10.4213/tmf9965 https://www.mathnet.ru/eng/tmf/v206/i1/p112
|
|