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

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:

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
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
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
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
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