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TMF, 2003, Volume 135, Number 3, Pages 515–523 (Mi tmf201)  

This article is cited in 5 scientific papers (total in 5 papers)

Periodic Gibbs Measures for the Ising Model with Competing Interactions

Kh. A. Nazarova, U. A. Rozikovb

a Samarkand State Institute of Architecture and Construction
b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: For the Ising model with competing interactions on the second-order Cayley tree, we find the operator corresponding to the periodic Gibbs distributions with period two and determine the invariant subsets of this operator, which are used to describe the periodic Gibbs distributions.

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

DOI: https://doi.org/10.4213/tmf201

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English version:
Theoretical and Mathematical Physics, 2003, 135:3, 881–888

Bibliographic databases:

Received: 22.05.2002

Citation: Kh. A. Nazarov, U. A. Rozikov, “Periodic Gibbs Measures for the Ising Model with Competing Interactions”, TMF, 135:3 (2003), 515–523; Theoret. and Math. Phys., 135:3 (2003), 881–888

Citation in format AMSBIB
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\by Kh.~A.~Nazarov, U.~A.~Rozikov
\paper Periodic Gibbs Measures for the Ising Model with Competing Interactions
\jour TMF
\yr 2003
\vol 135
\issue 3
\pages 515--523
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\crossref{https://doi.org/10.4213/tmf201}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1984454}
\zmath{https://zbmath.org/?q=an:1178.82019}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 135
\issue 3
\pages 881--888
\crossref{https://doi.org/10.1023/A:1024091206594}
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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. Rozikov, UA, “A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree”, Journal of Statistical Physics, 122:2 (2006), 217  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. U. A. Rozikov, M. M. Rakhmatullaev, “Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree”, Theoret. and Math. Phys., 160:3 (2009), 1292–1300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Rahmatullaev M.M., “Description of Weak Periodic Ground States of Ising Model with Competing Interactions on Cayley Tree”, Applied Mathematics & Information Sciences, 4:2 (2010), 237–251  mathscinet  zmath  isi
    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  scopus
    5. Akin H., “Gibbs Measures of An Ising Model With Competing Interactions on the Triangular Chandelier-Lattice”, Condens. Matter Phys., 22:2 (2019), 23002  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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