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TMF, 2020, Volume 204, Number 2, Pages 258–279 (Mi tmf9818)  

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

R. M. Khakimova, M. T. Makhammadalievb

a 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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9818

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

Bibliographic databases:

Received: 12.09.2019
Revised: 23.02.2020

Citation: R. M. Khakimov, M. T. Makhammadaliev, “Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model”, TMF, 204:2 (2020), 258–279; Theoret. and Math. Phys., 204:2 (2020), 1059–1078

Citation in format AMSBIB
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\by R.~M.~Khakimov, M.~T.~Makhammadaliev
\paper Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model
\jour TMF
\yr 2020
\vol 204
\issue 2
\pages 258--279
\mathnet{http://mi.mathnet.ru/tmf9818}
\crossref{https://doi.org/10.4213/tmf9818}
\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 204
\issue 2
\pages 1059--1078
\crossref{https://doi.org/10.1134/S0040577920080073}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85089740100}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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