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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 130, Number 1, Pages 109–118
DOI: https://doi.org/10.4213/tmf293 (Mi tmf293) 		 
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (237 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf293
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.
Received: 30.01.2001
Revised: 30.04.2001
English version:
Theoretical and Mathematical Physics, 2002, Volume 130, Issue 1, Pages 92–100
DOI: https://doi.org/10.1023/A:1013832632251
Bibliographic databases:
Language: Russian
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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\transl
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\vol 130
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\pages 92--100
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  • https://www.mathnet.ru/eng/tmf293
  • https://doi.org/10.4213/tmf293
  • https://www.mathnet.ru/eng/tmf/v130/i1/p109
    • This publication is cited in the following 4 articles:
    1. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    2. [Anonymous], “A Multi-Dimensional-Time Dynamical System”, Qual. Theor. Dyn. Syst., 12:2 (2013), 361–375  crossref  mathscinet  isi  scopus  scopus
    3. U. A. Rozikov, “System of recursive equations for the partition functions of 1D models”, Lobachevskii J Math, 32:2 (2011), 109  crossref
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:59
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