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 TMF, 1987, Volume 71, Number 3, Pages 426–440 (Mi tmf4972)

Phase diagrams and singularity at the point of a phase transition of the first kind in lattice gas models

S. N. Isakov

Abstract: Contour representation of the statistical sum of a $d$-dimensional $(d\geq 2)$ lattice gas models with the pair finite potential is studied. On the complex plane of the chemical potential $\mu$ the equation is found for the line of the phase transition of the first kind between two phases with the arbitrarily complicated periodic ordering of atoms of the lattice in the ground state in the assumption of the validity of Peierls' hypothesis. Inverse temperature $\beta=T^{-1}$ is also considered as complex and having a sufficiently large real part. Analyticity of the pressure outside the transition line is proved as well as the existence of finite limits of all derivatives of the pressure at $\mu$ going to the transition line. The explicit form of asymptotics of the limiting values of the derivatives $d^kp/d\mu^k\sim(k!)^{d/(d-1)}$ for real $\beta, \mu$ and large $k$ is found. It proves that the point of the first kind phase transition is an essentially singular point. Relation of the resut obtained to the properties of the system in metastable state is discussed.

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English version:
Theoretical and Mathematical Physics, 1987, 71:3, 638–648

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Citation: S. N. Isakov, “Phase diagrams and singularity at the point of a phase transition of the first kind in lattice gas models”, TMF, 71:3 (1987), 426–440; Theoret. and Math. Phys., 71:3 (1987), 638–648

Citation in format AMSBIB
\Bibitem{Isa87} \by S.~N.~Isakov \paper Phase diagrams and singularity at the point of a~phase transition of the first kind in lattice gas models \jour TMF \yr 1987 \vol 71 \issue 3 \pages 426--440 \mathnet{http://mi.mathnet.ru/tmf4972} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=910277} \transl \jour Theoret. and Math. Phys. \yr 1987 \vol 71 \issue 3 \pages 638--648 \crossref{https://doi.org/10.1007/BF01017098} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987L575800013} 

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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, “Interphase Hamiltonian and first-order phase transitions: A generalization of the Lee–Yang theorem”, Theoret. and Math. Phys., 153:1 (2007), 1434–1457
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