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TMF, 1984, Volume 61, Number 1, Pages 3–16 (Mi tmf5591)  

This article is cited in 1 scientific paper (total in 1 paper)

Infinite-range limit for correlation functions of lattice systems

L. A. Pastur, M. V. Shcherbina


Abstract: For a lattice Fermi gas, the quantum and classical Heisenberg models, and the Ising model it is shown that in the limit of an interaction of infinite range the correlation functions of these systems are identical to the expressions for them obtained in the self-consistent field approximation. The Lebowitz–Penrose theorem is also proved by a modified method of N. N. Bogolyubov (Jr). It is shown in the Appendix that the number of interacting harmonics in the method of the approximating Hamiltonian admits any growth less than the growth of the volume of the system.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 955–964

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Received: 11.11.1983

Citation: L. A. Pastur, M. V. Shcherbina, “Infinite-range limit for correlation functions of lattice systems”, TMF, 61:1 (1984), 3–16; Theoret. and Math. Phys., 61:1 (1984), 955–964

Citation in format AMSBIB
\Bibitem{PasShc84}
\by L.~A.~Pastur, M.~V.~Shcherbina
\paper Infinite-range limit for correlation functions of lattice systems
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 3--16
\mathnet{http://mi.mathnet.ru/tmf5591}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774202}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 955--964
\crossref{https://doi.org/10.1007/BF01038542}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AGK6100001}


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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. M. V. Shcherbina, “Classical Heisenberg model at zero temperature”, Theoret. and Math. Phys., 81:1 (1989), 1106–1113  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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