Geodesic
Gas of “connected configurations” and allowance for the “hard-core” potential of contours in the Mayer expansion of a gas of lattice-model contours
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 338-353 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\alpha(x)=\alpha_0\in G$. 
@article{TMF_1983_57_3_a1,
     author = {A. G. Basuev},
     title = {Gas of {\textquotedblleft}connected configurations{\textquotedblright} and allowance for the {\textquotedblleft}hard-core{\textquotedblright} potential of contours in the {Mayer} expansion of a~gas of lattice-model contours},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {338--353},
     year = {1983},
     volume = {57},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a1/}
}
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 338-353. http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a1/

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