V. N. Plechko, “Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals”, TMF, 64:1 (1985), 150–162; Theoret. and Math. Phys., 64:1 (1985), 748

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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 64, Number 1, Pages 150–162 (Mi tmf4908)

This article is cited in 42 scientific papers (total in 42 papers)

Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals

V. N. Plechko

Full-text PDF (1335 kB) Citations (42)

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Abstract: A simple method is proposed for exact solution of the two-dimensional Ising model on a torus (lattice of finite size with periodic boundary conditions). The problem is solved through construction of a Grassmann representation for the partition function. The mirror Grassmann factorization for the Boltzmann weights and a special identity for Grassmaan functions are used. The method is mathematically completely rigorous.

Received: 23.07.1984

English version:
Theoretical and Mathematical Physics, 1985, Volume 64, Issue 1, Pages 748–756
DOI: https://doi.org/10.1007/BF01017042

Bibliographic databases:

Language: Russian

Citation: V. N. Plechko, “Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals”, TMF, 64:1 (1985), 150–162; Theoret. and Math. Phys., 64:1 (1985), 748–756

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf4908

https://www.mathnet.ru/eng/tmf/v64/i1/p150

This publication is cited in the following 42 articles:

M. Ostilli, “The ignored Berezin's solution of the Ising model”, EPJ H, 50:1 (2025)
C. Wille, J. Eisert, A. Altland, “Topological dualities via tensor networks”, Phys. Rev. Research, 6:1 (2024)
Wojciech Niedziółka, Jacek Wojtkiewicz, “On nonintegrability of three-dimensional Ising model”, Reports on Mathematical Physics, 93:3 (2024), 271
Florian Kischel, Stefan Wessel, “Quantifying nonuniversal corner free-energy contributions in weakly anisotropic two-dimensional critical systems”, Phys. Rev. E, 110:2 (2024)
M. Ostilli, G. W. C. Rocha, C. G. Bezerra, G. M. Viswanathan, “Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices”, Sci Rep, 14:1 (2024)
F.A. Kassan-Ogly, “Spontaneous magnetization of Kagome lattice in Ising model”, Journal of Magnetism and Magnetic Materials, 572 (2023), 170568
G. M. Viswanathan, “Fermionic path integral for exact enumeration of polygons on the simple cubic lattice”, Phys. Rev. B, 108:1 (2023)
C Wetterich, “Cellular automaton for spinor gravity in four dimensions”, J. Phys.: Conf. Ser., 2533:1 (2023), 012016
C. Wetterich, “Fermionic quantum field theories as probabilistic cellular automata”, Phys. Rev. D, 105:7 (2022)
Christof Wetterich, “Quantum fermions from classical bits”, Phil. Trans. R. Soc. A., 380:2216 (2022)
Jean-Yves Fortin, “Singular self-energy for itinerant electrons in a dilute Ising spin bath”, J. Phys.: Condens. Matter, 33:8 (2021), 085602
Jean-Yves Fortin, Pierrick Lample, “Itinerant fermions on dilute frustrated Ising lattices”, Eur. Phys. J. B, 94:10 (2021)
Nahid Ghodratipour, Shahin Rouhani, “The Expectation Value of the Number of Loops and the Left-Passage Probability in the Double-Dimer Model”, Commun. Math. Phys., 373:1 (2020), 357
Amir Nourhani, Vincent H. Crespi, Paul E. Lammert, “Communicating through a sea of frustration: Zero-temperature triangular Ising antiferromagnet on a cylinder”, Phys. Rev. E, 98:3 (2018)
Nicolas Allegra, “Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics”, Nuclear Physics B, 894 (2015), 685
Nicolas Allegra, Jean-Yves Fortin, “Grassmannian representation of the two-dimensional monomer-dimer model”, Phys. Rev. E, 89:6 (2014)
Gibbs Measures and Phase Transitions, 2011, 495
V. N. Plechko, “Fermions and disorder in ising and related models in two dimensions”, Phys. Part. Nuclei, 41:7 (2010), 1054
S. AKBAR JAFARI, “GRAPHICAL SOLUTION OF THE ISING MODEL ON HONEYCOMB LATTICE”, Int. J. Mod. Phys. B, 23:03 (2009), 395
Maxime Clusel, Jean-Yves Fortin, Vladimir N Plechko, “Alternative description of the 2D Blume–Capel model using Grassmann algebra”, J. Phys. A: Math. Theor., 41:40 (2008), 405004

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

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