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TMF, 2015, Volume 183, Number 3, Pages 441–449 (Mi tmf8700)  

This article is cited in 3 scientific papers (total in 3 papers)

Translation-invariant Gibbs measures for fertile three-state “hard core” models on a Cayley tree

R. M. Khakimov

Institute for Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We consider fertile three-state "hard core" models with the activity parameter $\lambda>0$ on an order-three Cayley tree. It is known that there exist four types of such models: in two of them, the translation-invariant Gibbs measure is unique for $\lambda>0$, and in the other two, a value $\lambda_\mathrm{cr}$ is found such that there exist only three translation-invariant Gibbs measures for $\lambda>\lambda_\mathrm{cr}$ and a single translation-invariant Gibbs measure for $\lambda\le\lambda_\mathrm{cr}$.

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

DOI: https://doi.org/10.4213/tmf8700

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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 829–835

Bibliographic databases:

Received: 30.04.2014
Revised: 17.09.2014

Citation: R. M. Khakimov, “Translation-invariant Gibbs measures for fertile three-state “hard core” models on a Cayley tree”, TMF, 183:3 (2015), 441–449; Theoret. and Math. Phys., 183:3 (2015), 829–835

Citation in format AMSBIB
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\by R.~M.~Khakimov
\paper Translation-invariant Gibbs measures for fertile three-state ``hard core'' models on a~Cayley tree
\jour TMF
\yr 2015
\vol 183
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\pages 441--449
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\jour Theoret. and Math. Phys.
\yr 2015
\vol 183
\issue 3
\pages 829--835
\crossref{https://doi.org/10.1007/s11232-015-0299-6}
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  • https://doi.org/10.4213/tmf8700
  • http://mi.mathnet.ru/eng/tmf/v183/i3/p441

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. M. Khakimov, “Gibbs measures for fertile hard-core models on the Cayley tree”, Theoret. and Math. Phys., 186:2 (2016), 294–305  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. R. M. Khakimov, “Weakly periodic Gibbs measures for HC-models on Cayley trees”, Siberian Math. J., 59:1 (2018), 147–156  mathnet  crossref  crossref  isi  elib
    3. Kissel S., Kuelske C., Rozikov U.A., “Hard-Core and Soft-Core Widom-Rowlinson Models on Cayley Trees”, J. Stat. Mech.-Theory Exp., 2019, 043204  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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