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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 149, Number 2, Pages 281–298
DOI: https://doi.org/10.4213/tmf4234 (Mi tmf4234) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Two-dimensional four-line models of the Ising model type

V. V. Katrakhov, Yu. N. Kharchenko

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (773 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf4234
Abstract: We briefly describe the theory of root transfer matrices for four-line models with the field in the new indexless form. We use theoretical and numerical methods to reveal new effects in the theory of singular points and phase transitions. A substantial part of the results is obtained using a numerical algorithm that drastically {(}at least exponentially{\rm)} reduces the computational complexity of Ising-type models by using the extremely sparse root transfer matrix.
Keywords: Ising model, transfer matrix, partition function, ferromagnet, antiferromagnet, free energy, magnetization, magnetic susceptibility, critical point, singular curve, phase transition.
Received: 02.12.2004
Revised: 17.04.2006
English version:
Theoretical and Mathematical Physics, 2006, Volume 149, Issue 2, Pages 1545–1558
DOI: https://doi.org/10.1007/s11232-006-0137-y
Bibliographic databases:
Language: Russian
Citation: V. V. Katrakhov, Yu. N. Kharchenko, “Two-dimensional four-line models of the Ising model type”, TMF, 149:2 (2006), 281–298; Theoret. and Math. Phys., 149:2 (2006), 1545–1558
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf4234
  • https://doi.org/10.4213/tmf4234
  • https://www.mathnet.ru/eng/tmf/v149/i2/p281
    • This publication is cited in the following 3 articles:
    1. Yu. N. Kharchenko, “Reshenie odnomernykh modelei reshetochnogo gaza”, Dalnevost. matem. zhurn., 19:2 (2019), 245–255  mathnet
    2. G. Sh. Tsitsiashvili, “Itogi nauchnoi deyatelnosti laboratorii veroyatnostnykh metodov i sistemnogo analiza IPM DVO RAN za 1988–2008 gg.”, Dalnevost. matem. zhurn., 8:1 (2008), 111–120  mathnet
    3. Yu. N. Kharchenko, “Nekotorye svoistva kornevykh transfer-matrits vosmivershinnykh modelei”, Dalnevost. matem. zhurn., 8:2 (2008), 218–222  mathnet
    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:66
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