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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
$d^kp/d\mu^k\sim(k!)^{d/(d1)}$ 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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Theoretical and Mathematical Physics, 1987, 71:3, 638–648
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Received: 05.12.1985
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 426440
\mathnet{http://mi.mathnet.ru/tmf4972}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=910277}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 71
\issue 3
\pages 638648
\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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http://mi.mathnet.ru/eng/tmf4972 http://mi.mathnet.ru/eng/tmf/v71/i3/p426
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This publication is cited in the following articles:

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

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