
This article is cited in 5 scientific papers (total in 5 papers)
Complete phase diagrams with respect to external fields at low temperatures for models with nearestneighbor interaction in the case of a finite or countable number of ground states
A. G. Basuev^{}
Abstract:
It is shown that at low temperatures and for arbitrary external
fields (activities $z_k$, $\hat z=ż_k\}$) the ensemble with the
Hamiltonian (1) and particles in the set $\Phi$ is equivalent to
$\Phi$ Ising models with activities $b_k(\hat z), \hat b(\hat z)
= \{b_k(\hat z)\}$. The mapping $\hat b(\hat z)$ is a
homeomorphism on the positive octant $l_\infty (\Phi)$ if
$\sup\limits_k \sum\limits_{l \neq k}
\exp\{\beta\varepsilon(k,l)\}\leq \bar\psi_1$, where $\bar\psi_1$
is a small number. The pressure in the ensemble is $p(\hat
z)=\sup\limits_{k \in \Phi}b_k(\hat z) =  \hat b(\hat z) $. The
limit Gibbs states corresponding to the vector $\hat z$ are small
perturbations of the ground states $\alpha(x)= q \in G_1(\hat z)$
and are labeled by elements of the set $G_1(\hat z) = \{ \hat q:
\ln b_q(\hat z) = p(\hat z)\}$, where the function $G_1(\hat z)$
defines the phase diagram of the ensemble. In the regions of
constancy of $G_1(\hat z)$ the pressure can be continued to a
holomorphie function, and the particle densities $z_l \partial
p/\partial z_l$ are continuous in the closure of a region of
constancy of $G_1(\hat z)$.
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Theoretical and Mathematical Physics, 1984, 58:2, 171–182
Bibliographic databases:
Received: 19.05.1983
Citation:
A. G. Basuev, “Complete phase diagrams with respect to external fields at low temperatures for models with nearestneighbor interaction in the case of a finite or countable number of ground states”, TMF, 58:2 (1984), 261–278; Theoret. and Math. Phys., 58:2 (1984), 171–182
Citation in format AMSBIB
\Bibitem{Bas84}
\by A.~G.~Basuev
\paper Complete phase diagrams with respect to external fields at low temperatures for models with nearestneighbor interaction in the case of a finite or countable number of ground states
\jour TMF
\yr 1984
\vol 58
\issue 2
\pages 261278
\mathnet{http://mi.mathnet.ru/tmf4526}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=743412}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 58
\issue 2
\pages 171182
\crossref{https://doi.org/10.1007/BF01017924}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TG27600012}
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http://mi.mathnet.ru/eng/tmf4526 http://mi.mathnet.ru/eng/tmf/v58/i2/p261
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This publication is cited in the following articles:

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

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

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

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

A. G. Basuev, “Ising model in halfspace: A series of phase transitions in low
magnetic fields”, Theoret. and Math. Phys., 153:2 (2007), 1539–1574

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