This article is cited in 8 papers

Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model

R. M. Khakimov^a, M. T. Makhammadaliev<sup>b

a</sup> Namangan Department, Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Namangan, Uzbekistan
^b Namangan State University, Namangan, Uzbekistan

Abstract: We study a "hard-core" model on a Cayley tree. In the case of a normal divisor of index 4, we show the uniqueness of weakly periodic Gibbs measures under certain conditions on the parameters. Moreover, we prove that there exist weakly periodic (nonperiodic) Gibbs measures different from those previously known.

Keywords: Cayley tree, configuration, hard-core model, Gibbs measure, translation-invariant measure, periodic measure, weakly periodic measure.

Received: 12.09.2019
Revised: 23.02.2020

DOI: 10.4213/tmf9818

 English version: Theoretical and Mathematical Physics, 2020, 204:2, 1059–1078

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