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TMF, 1983, Volume 54, Number 1, Pages 8–22 (Mi tmf4360)  

This article is cited in 8 scientific papers (total in 10 papers)

A statistical physics model

V. S. Vladimirov, I. V. Volovich


Abstract: A Gaussian model on a half-axis with interaction given by a Toeptitz form is considered. The free energy and correlation functions are calculated. A new method of inverting Toeplitz matrices and solving the generalized Wiener-Hopf problem is used. The asymptotic behavior of the correlation functions is studied and the conditions for the presence or absence of long-range order are established. The free energyand correlation functions are calculated for a Gaussian model with external field. An expression is obtained for the free energy of a multidimensional Gaussian model.

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English version:
Theoretical and Mathematical Physics, 1983, 54:1, 1–12

Bibliographic databases:

Document Type: Article
Received: 07.07.1982

Citation: V. S. Vladimirov, I. V. Volovich, “A statistical physics model”, TMF, 54:1 (1983), 8–22; Theoret. and Math. Phys., 54:1 (1983), 1–12

Citation in format AMSBIB
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\by V.~S.~Vladimirov, I.~V.~Volovich
\paper A~statistical physics model
\jour TMF
\yr 1983
\vol 54
\issue 1
\pages 8--22
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=704006}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 54
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1007/BF01017118}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RF77900001}


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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. N. N. Bogolyubov, A. A. Logunov, G. I. Marchuk, “Vasilii Sergeevich Vladimirov (on his sixtieth birthday)”, Russian Math. Surveys, 38:1 (1983), 231–243  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. L. Sakhnovich, I. M. Spitkovsky, “Block-Toeplitz matrices and associated properties of a Gaussian model on a half-axis”, Theoret. and Math. Phys., 63:1 (1985), 427–431  mathnet  crossref  mathscinet  zmath  isi
    3. N. K. Fazlutdinov, “One-dimensional lattice models with nonsummable interaction”, Theoret. and Math. Phys., 63:2 (1985), 535–538  mathnet  crossref  mathscinet  isi
    4. N. S. Gonchar, “Solvability of a class of systems of infinite-dimensional integral equations and their application in statistical mechanics”, Theoret. and Math. Phys., 64:3 (1985), 949–959  mathnet  crossref  mathscinet  isi
    5. A. L. Sakhnovich, “On a class of extremal problems”, Math. USSR-Izv., 30:2 (1988), 411–418  mathnet  crossref  mathscinet  zmath
    6. V. S. Vladimirov, “The Wiener–Hopf equation in Nevanlinna and Smirnov algebras”, Math. USSR-Izv., 31:1 (1988), 77–94  mathnet  crossref  mathscinet  zmath
    7. V. M. Adamyan, “Some limit relations for multidimensional positive-definite toeplitz matrices”, Funct. Anal. Appl., 22:1 (1988), 44–45  mathnet  crossref  mathscinet  zmath  isi
    8. V. B. Dybin, “The Wiener–Hopf equation and Blaschke products”, Math. USSR-Sb., 70:1 (1991), 205–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. L. Sakhnovich, “Spectral functions of a canonical system of order $2n$”, Math. USSR-Sb., 71:2 (1992), 355–369  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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