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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 183, Number 3, Pages 434–440
DOI: https://doi.org/10.4213/tmf8796 (Mi tmf8796) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree

M. M. Rakhmatullaev

Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
Full-text PDF (365 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf8796
Abstract: We study weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree. We prove that under some conditions on the model parameters, there exist at least two weakly periodic Gibbs measures for the antiferromagnetic Ising model with an external field.
Keywords: Cayley tree, Gibbs measure, Ising model with external field, weakly periodic measure.
Received: 17.09.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 183, Issue 3, Pages 822–828
DOI: https://doi.org/10.1007/s11232-015-0298-7
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. M. Rakhmatullaev, “Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree”, TMF, 183:3 (2015), 434–440; Theoret. and Math. Phys., 183:3 (2015), 822–828
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8796
  • https://doi.org/10.4213/tmf8796
  • https://www.mathnet.ru/eng/tmf/v183/i3/p434
    • This publication is cited in the following 3 articles:
    1. Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova, “On H-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree”, Reports on Mathematical Physics, 95:1 (2025), 93  crossref
    2. M. M. Rahmatullaev, Zh. D. Dekhkonov, “Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order $k=2$”, Theoret. and Math. Phys., 206:2 (2021), 185–198  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. M. M. Rakhmatullaev, Zh. D. Dekhkonov, “Suschestvovanie slabo periodicheskikh mer Gibbsa dlya modeli Izinga na dereve Keli poryadka tri”, Vladikavk. matem. zhurn., 23:4 (2021), 77–88  mathnet  crossref
    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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    Full-text PDF :157
    References:60
    First page:8
     
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