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TMF, 2002, Volume 130, Number 1, Pages 109–118 (Mi tmf293)  

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

Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We describe a wide class of normal divisors of infinite index of the group representation of the Cayley tree and study the structure of partitions of the Cayley tree w.r.t. any normal divisor of infinite index. We prove that for a specific normal divisor of infinite index, there are three periodic and uncountably many nonperiodic Gibbs measures for an inhomogeneous Ising model.

DOI: https://doi.org/10.4213/tmf293

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English version:
Theoretical and Mathematical Physics, 2002, 130:1, 92–100

Bibliographic databases:

Received: 30.01.2001
Revised: 30.04.2001

Citation: U. A. Rozikov, “Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree”, TMF, 130:1 (2002), 109–118; Theoret. and Math. Phys., 130:1 (2002), 92–100

Citation in format AMSBIB
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\by U.~A.~Rozikov
\paper Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree
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\vol 130
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 130
\issue 1
\pages 92--100
\crossref{https://doi.org/10.1023/A:1013832632251}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Rozikov U.A., Ishankulov F.T., “Description of periodic p-harmonic functions on Cayley tree”, Nodea-Nonlinear Differential Equations and Applications, 17:2 (2010), 153–160  crossref  mathscinet  zmath  isi  scopus  scopus
    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. [Anonymous], “A Multi-Dimensional-Time Dynamical System”, Qual. Theor. Dyn. Syst., 12:2 (2013), 361–375  crossref  mathscinet  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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