|
This article is cited in 11 scientific papers (total in 11 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:
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
\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/izv251}
\crossref{https://doi.org/10.4213/im251}
\mathscinet{http://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000084502900005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0141450646}
Linking options:
http://mi.mathnet.ru/eng/izv251https://doi.org/10.4213/im251 http://mi.mathnet.ru/eng/izv/v63/i4/p79
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:
-
Yu. M. Zinoviev, “Ising Model and $L$-Function”, Theoret. and Math. Phys., 126:1 (2001), 66–80
-
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
-
Yu. M. Zinoviev, “Spontaneous Magnetization in the Two-Dimensional Ising Model”, Theoret. and Math. Phys., 136:3 (2003), 1280–1296
-
Yu. M. Zinoviev, “Pfaffian and the Kac–Ward Formula in the Two-Dimensional Ising Model”, Proc. Steklov Inst. Math., 251 (2005), 132–145
-
Cimasoni D., “A generalized Kac-Ward formula”, Journal of Statistical Mechanics-Theory and Experiment, 2010, P07023
-
Cimasoni D., “The Critical Ising Model via Kac-Ward Matrices”, Commun. Math. Phys., 316:1 (2012), 99–126
-
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
-
Lis M., “Phase Transition Free Regions in the Ising Model Via the Kac-Ward Operator”, Commun. Math. Phys., 331:3 (2014), 1071–1086
-
Lis M., “Short Proof of the Kac-Ward Formula”, Ann. Inst. Henri Poincare D, 3:1 (2016), 45–53
-
Chelkak D., Cimasoni D., Kassel A., “Revisiting the Combinatorics of the 2D Ising Model”, Ann. Inst. Henri Poincare D, 4:3 (2017), 309–385
-
Lis M., “Circle Patterns and Critical Ising Models”, Commun. Math. Phys., 370:2 (2019), 507–530
|
Number of views: |
This page: | 671 | Full text: | 238 | References: | 52 | First page: | 6 |
|