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TMF, 2006, Volume 149, Number 1, Pages 18–31 (Mi tmf3825)  

This article is cited in 7 scientific papers (total in 7 papers)

Gibbs measures for the SOS model with four states on a Cayley tree

U. A. Rozikov, Sh. A. Shoyusupov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We analyze the SOS {(}solid-on-solid{\rm)} model with spins 0, 1, 2, 3 on a Cayley tree of order $k\ge 1$. We consider translation-invariant and periodic splitting Gibbs measures for this model. The majority of the constructed Gibbs measures are mirror symmetric.

Keywords: Cayley tree, configuration, Gibbs measure, periodic Gibbs measure

DOI: https://doi.org/10.4213/tmf3825

Full text: PDF file (465 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 149:1, 1312–1323

Bibliographic databases:

Received: 16.01.2006
Revised: 29.03.2006

Citation: U. A. Rozikov, Sh. A. Shoyusupov, “Gibbs measures for the SOS model with four states on a Cayley tree”, TMF, 149:1 (2006), 18–31; Theoret. and Math. Phys., 149:1 (2006), 1312–1323

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf3825
  • http://mi.mathnet.ru/eng/tmf/v149/i1/p18

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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, M. M. Rakhmatullaev, “Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree”, Theoret. and Math. Phys., 156:2 (2008), 1218–1227  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. U. A. Rozikov, Sh. A. Shoyusupov, “Fertile HC models with three states on a Cayley tree”, Theoret. and Math. Phys., 156:3 (2008), 1319–1330  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Rozikov UA, “A contour method on Cayley trees”, Journal of Statistical Physics, 130:4 (2008), 801–813  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    5. R. M. Khakimov, “Translation-invariant Gibbs measures for fertile three-state “hard core” models on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 829–835  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Kuelske C., Rozikov U.A., “Extremality of Translation-Invariant Phases For a Three-State Sos-Model on the Binary Tree”, J. Stat. Phys., 160:3 (2015), 659–680  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. 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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