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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 3(147), Pages 3–22 (Mi umn5495)  

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

The plane Ising model

F. A. Berezin


Abstract: In this paper the statistical sum of a plane Ising model in the absence of an external magnetic field is computed.

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English version:
Russian Mathematical Surveys, 1969, 24:3, 1–22

Bibliographic databases:

UDC: 519.284
MSC: 82B20, 82B05, 82B30
Received: 07.02.1969

Citation: F. A. Berezin, “The plane Ising model”, Uspekhi Mat. Nauk, 24:3(147) (1969), 3–22; Russian Math. Surveys, 24:3 (1969), 1–22

Citation in format AMSBIB
\Bibitem{Ber69}
\by F.~A.~Berezin
\paper The plane Ising model
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 3(147)
\pages 3--22
\mathnet{http://mi.mathnet.ru/umn5495}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=252005}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 3
\pages 1--22
\crossref{https://doi.org/10.1070/RM1969v024n03ABEH001346}


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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. F. A. Berezin, “The number of closed nonselfintersecting contours on a planar lattice”, Math. USSR-Sb., 14:1 (1971), 47–63  mathnet  crossref  mathscinet  zmath
    2. B. N. Valuev, “Realization of an integral with respect to anticommuting variables”, Theoret. and Math. Phys., 40:1 (1979), 593–596  mathnet  crossref  mathscinet  zmath  isi
    3. V. N. Plechko, “Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals”, Theoret. and Math. Phys., 64:1 (1985), 748–756  mathnet  crossref  mathscinet  isi
    4. M. P. Zhelifonov, B. S. Nikitin, “Exact solution for the partition function of a system of interacting fermions”, Theoret. and Math. Phys., 68:1 (1986), 707–714  mathnet  crossref  mathscinet  isi
    5. V. A. Klimenko, “Summation of closed diagrams on a square lattice”, Theoret. and Math. Phys., 83:2 (1990), 553–556  mathnet  crossref  mathscinet  isi
    6. Y. A. Bugrij, “Solution of 2D Ising model on triangular lattice by auxiliary $q$-deformed Grassmann field method”, Theoret. and Math. Phys., 109:3 (1996), 1590–1607  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. G F De Angelis, G Jona-Lasinio, V Sidoravicius, J Phys A Math Gen, 31:1 (1998), 289  crossref  mathscinet  zmath  adsnasa  isi
    8. Massimo Ostilli, “On the probabilistic approach for Gaussian Berezin integrals”, Annals of Physics, 308:2 (2003), 555  crossref
    9. V. N. Plechko, “Fermions and disorder in ising and related models in two dimensions”, Phys. Part. Nuclei, 41:7 (2010), 1054  crossref
    10. V. M. Kaplitskii, “Thermodynamical averages for the Ising model and spectral invariants of Toeplitz matrices”, Theoret. and Math. Phys., 203:3 (2020), 780–793  mathnet  crossref  crossref  mathscinet  isi  elib
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