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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 4, Pages 79–100 (Mi izv251)  

This article is cited in 10 scientific papers (total in 10 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

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.

DOI: https://doi.org/10.4213/im251

Full text: PDF file (2112 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1999, 63:4, 707–727

Bibliographic databases:

Document Type: Article
MSC: 57N05, 82B20, 55N10
Received: 25.12.1997

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
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\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
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\jour Izv. Math.
\yr 1999
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  • https://doi.org/10.4213/im251
  • http://mi.mathnet.ru/eng/izv/v63/i4/p79

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. M. Zinoviev, “Ising Model and $L$-Function”, Theoret. and Math. Phys., 126:1 (2001), 66–80  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Yu. M. Zinoviev, “The Three-Dimensional ${\mathbb Z}_{2}$ Electrodynamics and the Two-Dimensional Ising Model”, Theoret. and Math. Phys., 132:1 (2002), 1000–1011  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Yu. M. Zinoviev, “Spontaneous Magnetization in the Two-Dimensional Ising Model”, Theoret. and Math. Phys., 136:3 (2003), 1280–1296  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Yu. M. Zinoviev, “Pfaffian and the Kac–Ward Formula in the Two-Dimensional Ising Model”, Proc. Steklov Inst. Math., 251 (2005), 132–145  mathnet  mathscinet  zmath
    5. Cimasoni D., “A generalized Kac-Ward formula”, Journal of Statistical Mechanics-Theory and Experiment, 2010, P07023  crossref  isi  scopus
    6. Cimasoni D., “The Critical Ising Model via Kac-Ward Matrices”, Commun. Math. Phys., 316:1 (2012), 99–126  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Kager W., Lis M., Meester R., “The Signed Loop Approach to the Ising Model: Foundations and Critical Point”, J. Stat. Phys., 152:2 (2013), 353–387  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Lis M., “Phase Transition Free Regions in the Ising Model Via the Kac-Ward Operator”, Commun. Math. Phys., 331:3 (2014), 1071–1086  crossref  mathscinet  zmath  isi  scopus
    9. Lis M., “Short Proof of the Kac-Ward Formula”, Ann. Inst. Henri Poincare D, 3:1 (2016), 45–53  crossref  mathscinet  zmath  isi  scopus
    10. Chelkak D., Cimasoni D., Kassel A., “Revisiting the Combinatorics of the 2D Ising Model”, Ann. Inst. Henri Poincare D, 4:3 (2017), 309–385  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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