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

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:

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
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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
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
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
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
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
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