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TMF, 1983, Volume 57, Number 3, Pages 338–353 (Mi tmf2286)  

This article is cited in 4 scientific papers (total in 4 papers)

Gas of “connected configurations” and allowance for the “hard-core” potential of contours in the Mayer expansion of a gas of lattice-model contours

A. G. Basuev


Abstract: A theorem is proved that makes it possible to take into account the “hard-core” potential of contours and reduce the study of the convergence of the Mayer expansions of the gas of contours to the remaining part of the interaction. In particular, for a model with nearest-neighbor interaction, in which
$$ U(\alpha)=\sum_{|x-y|=1}\varepsilon(\alpha(x)\alpha^{-1}(y)), $$
$\alpha(x)$ takes values in the discrete group $G$ with identity $e$, $\varepsilon(\alpha)=\varepsilon(\alpha^{-1})$ $\forall\alpha\ne e$, $\varepsilon(e)=0$ and
$$ \sum_{\alpha\in G\setminus e}\exp\{-\beta U(\alpha)\} \underset{\beta\to\infty}\longrightarrow0, $$
the existence is proved of not less than $|G|$ ($|G|\leqslant\infty$) limit Gibbs distributions, which are small perturbations of the ground states $\alpha(x)=\alpha_0\in G$.

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English version:
Theoretical and Mathematical Physics, 1983, 57:3, 1178–1189

Bibliographic databases:

Received: 22.02.1983

Citation: A. G. Basuev, “Gas of “connected configurations” and allowance for the “hard-core” potential of contours in the Mayer expansion of a gas of lattice-model contours”, TMF, 57:3 (1983), 338–353; Theoret. and Math. Phys., 57:3 (1983), 1178–1189

Citation in format AMSBIB
\Bibitem{Bas83}
\by A.~G.~Basuev
\paper Gas of ``connected configurations'' and allowance for the ``hard-core'' potential of contours in the Mayer expansion of a~gas of lattice-model contours
\jour TMF
\yr 1983
\vol 57
\issue 3
\pages 338--353
\mathnet{http://mi.mathnet.ru/tmf2286}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=735393}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 57
\issue 3
\pages 1178--1189
\crossref{https://doi.org/10.1007/BF01018744}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SY87100002}


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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. A. G. Basuev, “Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model”, Theoret. and Math. Phys., 58:1 (1984), 80–91  mathnet  crossref  mathscinet  isi
    2. A. G. Basuev, “Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states”, Theoret. and Math. Phys., 58:2 (1984), 171–182  mathnet  crossref  mathscinet  isi
    3. A. G. Basuev, “Hamiltonian of the phase separation border and phase transitions of the first kind. I”, Theoret. and Math. Phys., 64:1 (1985), 716–734  mathnet  crossref  mathscinet  isi
    4. A. G. Basuev, “Hamiltonian of the phase separation border and phase transitions of the first kind. II. The simplest disordered phases”, Theoret. and Math. Phys., 72:2 (1987), 861–871  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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