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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
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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
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\pages 79--100
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http://mi.mathnet.ru/eng/izv251https://doi.org/10.4213/im251 http://mi.mathnet.ru/eng/izv/v63/i4/p79
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Yu. M. Zinoviev, “Ising Model and $L$-Function”, Theoret. and Math. Phys., 126:1 (2001), 66–80
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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
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Yu. M. Zinoviev, “Spontaneous Magnetization in the Two-Dimensional Ising Model”, Theoret. and Math. Phys., 136:3 (2003), 1280–1296
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Yu. M. Zinoviev, “Pfaffian and the Kac–Ward Formula in the Two-Dimensional Ising Model”, Proc. Steklov Inst. Math., 251 (2005), 132–145
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Cimasoni D., “A generalized Kac-Ward formula”, Journal of Statistical Mechanics-Theory and Experiment, 2010, P07023
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Cimasoni D., “The Critical Ising Model via Kac-Ward Matrices”, Commun. Math. Phys., 316:1 (2012), 99–126
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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
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Lis M., “Phase Transition Free Regions in the Ising Model Via the Kac-Ward Operator”, Commun. Math. Phys., 331:3 (2014), 1071–1086
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Lis M., “Short Proof of the Kac-Ward Formula”, Ann. Inst. Henri Poincare D, 3:1 (2016), 45–53
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Chelkak D., Cimasoni D., Kassel A., “Revisiting the Combinatorics of the 2D Ising Model”, Ann. Inst. Henri Poincare D, 4:3 (2017), 309–385
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Lis M., “Circle Patterns and Critical Ising Models”, Commun. Math. Phys., 370:2 (2019), 507–530
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