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Izvestiya: Mathematics, 1999, Volume 63, Issue 4, Pages 707–727
DOI: https://doi.org/10.1070/im1999v063n04ABEH000251 (Mi im251) 		 
This article is cited in 14 scientific papers (total in 14 papers)

The two-dimensional Ising model and the Kac–Ward determinant

N. P. Dolbilina, Yu. M. Zinovieva, A. S. Mishchenkob, M. A. Shtan'koa, M. I. Shtogrina

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University
English version PDF (441 kB) Citations (14)
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DOI: https://doi.org/10.1070/im1999v063n04ABEH000251
Abstract: We prove a formula that expresses the square of the statistical sum for the two-dimensional Ising model for an arbitrary plane lattice in terms of the determinant of a matrix similar to the Kac–Ward matrix.
Received: 25.12.1997
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1999, Volume 63, Issue 4, Pages 79–100
DOI: https://doi.org/10.4213/im251
Bibliographic databases:
Document Type: Article
MSC: 57N05, 82B20, 55N10
Language: English
Original paper language: Russian
Citation: N. P. Dolbilin, Yu. M. Zinoviev, A. S. Mishchenko, M. A. Shtan'ko, M. I. Shtogrin, “The two-dimensional Ising model and the Kac–Ward determinant”, Izv. RAN. Ser. Mat., 63:4 (1999), 79–100; Izv. Math., 63:4 (1999), 707–727
Citation in format AMSBIB
\Bibitem{DolZinMis99}
\by N.~P.~Dolbilin, Yu.~M.~Zinoviev, A.~S.~Mishchenko, M.~A.~Shtan'ko, M.~I.~Shtogrin
\paper The two-dimensional Ising model and the Kac--Ward determinant
\jour Izv. RAN. Ser. Mat.
\yr 1999
\vol 63
\issue 4
\pages 79--100
\mathnet{http://mi.mathnet.ru/im251}
\crossref{https://doi.org/10.4213/im251}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1717680}
\zmath{https://zbmath.org/?q=an:0990.82003}
\transl
\jour Izv. Math.
\yr 1999
\vol 63
\issue 4
\pages 707--727
\crossref{https://doi.org/10.1070/im1999v063n04ABEH000251}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000084502900005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0141450646}
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  • https://www.mathnet.ru/eng/im/v63/i4/p79
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:87
    First page:6
     
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