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TMF, 2008, Volume 156, Number 3, Pages 412–424 (Mi tmf6256)  

This article is cited in 11 scientific papers (total in 11 papers)

Fertile HC models with three states on a Cayley tree

U. A. Rozikovab, Sh. A. Shoyusupova

a Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
b GC University, Abdus Salam School of Mathematical Sciences

Abstract: We consider fertile hard-core (HC) models with three states on a homogeneous Cayley tree. It is known that four types of such models exist. For these models, we describe the translation-invariant and periodic HC Gibbs measures. We also construct a uncountable set of nonperiodic Gibbs measures.

Keywords: Cayley tree, configuration, HC model, Gibbs measure

DOI: https://doi.org/10.4213/tmf6256

Full text: PDF file (484 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 156:3, 1319–1330

Bibliographic databases:

Received: 10.07.2007

Citation: U. A. Rozikov, Sh. A. Shoyusupov, “Fertile HC models with three states on a Cayley tree”, TMF, 156:3 (2008), 412–424; Theoret. and Math. Phys., 156:3 (2008), 1319–1330

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v156/i3/p412

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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. U. A. Rozikov, R. M. Khakimov, “The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model”, Theoret. and Math. Phys., 173:1 (2012), 1377–1386  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    3. O. N. Khakimov, “$p$-Adic Gibbs measures for the hard core model with three states on the Cayley tree”, Theoret. and Math. Phys., 177:1 (2013), 1339–1351  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Rozikov U.A. Akin H. Uguz S., “Exact Solution of a Generalized Annni Model on a Cayley Tree”, Math. Phys. Anal. Geom., 17:1-2 (2014), 103–114  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Rustam M. Khakimov, “The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree”, Zhurn. SFU. Ser. Matem. i fiz., 8:2 (2015), 165–172  mathnet
    6. Rozikov U.A., Khakimov R.M., “Gibbs Measures For the Fertile Three-State Hard-Core Models on a Cayley Tree”, Queueing Syst., 81:1 (2015), 49–69  crossref  mathscinet  zmath  isi  scopus  scopus
    7. 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
    8. O. N. Khakimov, “A $p$-adic hard-core model with three states on a Cayley tree”, Siberian Math. J., 57:4 (2016), 726–734  mathnet  crossref  crossref  isi  elib
    9. Gandolfo D. Rozikov U.A. Ruiz J., “on Four State Hard Core Models on the Cayley Tree”, Markov Process. Relat. Fields, 22:2 (2016), 359–377  mathscinet  zmath  isi
    10. 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
    11. 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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