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TMF, 1984, Volume 58, Number 2, Pages 261–278 (Mi tmf4526)  

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 nearest-neighbor 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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English version:
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 nearest-neighbor 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 nearest-neighbor interaction in the case of a finite or countable number of ground states
\jour TMF
\yr 1984
\vol 58
\issue 2
\pages 261--278
\mathnet{http://mi.mathnet.ru/tmf4526}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=743412}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 58
\issue 2
\pages 171--182
\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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    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, “Hamiltonian of the phase separation border and phase transitions of the first kind. I”, Theoret. and Math. Phys., 64:1 (1985), 716–734  mathnet  crossref  mathscinet  isi
    2. 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  mathnet  crossref  mathscinet  isi
    3. 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  mathnet  crossref  mathscinet  isi
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. A. G. Basuev, “Ising model in half-space: A series of phase transitions in low magnetic fields”, Theoret. and Math. Phys., 153:2 (2007), 1539–1574  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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