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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 2, Pages 448–462 (Mi izv2119)  

This article is cited in 5 scientific papers (total in 5 papers)

Conditions for the nonuniqueness of the Gibbs state for lattice models having finite interaction potentials

V. M. Gercik


Abstract: The nonuniqueness of the Gibbs state is demonstrated for discrete lattice models having finite periodic interaction potentials which obey the so-called Peierls' condition. The limit points of the set of Gibbs states correspond to the periodic ground states for the models, which compose an orbit relative to the group of transformations leaving the potential invariant. The proof is based on a deduction of Peierls' estimates for the corresponding outer boundaries.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:2, 429–443

Bibliographic databases:

UDC: 519.2
MSC: 82A40
Received: 22.10.1974

Citation: V. M. Gercik, “Conditions for the nonuniqueness of the Gibbs state for lattice models having finite interaction potentials”, Izv. Akad. Nauk SSSR Ser. Mat., 40:2 (1976), 448–462; Math. USSR-Izv., 10:2 (1976), 429–443

Citation in format AMSBIB
\Bibitem{Ger76}
\by V.~M.~Gercik
\paper Conditions for the nonuniqueness of the Gibbs state for lattice models having
finite interaction potentials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 2
\pages 448--462
\mathnet{http://mi.mathnet.ru/izv2119}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=418790}
\zmath{https://zbmath.org/?q=an:0365.60120}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 2
\pages 429--443
\crossref{https://doi.org/10.1070/IM1976v010n02ABEH001702}


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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. S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems continuation”, Theoret. and Math. Phys., 26:1 (1976), 39–49  mathnet  crossref  mathscinet
    2. 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”, Theoret. and Math. Phys., 58:2 (1984), 171–182  mathnet  crossref  mathscinet  isi
    3. D. G. Martirosyan, “Uniqueness of Gibbs states in lattice models with one ground state”, Theoret. and Math. Phys., 63:2 (1985), 511–518  mathnet  crossref  mathscinet  isi
    4. 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
    5. Eugene Pechersky, Elena Petrova, Sergey Pirogov, “Phase transitions of laminated models at any temperature”, Mosc. Math. J., 10:4 (2010), 789–806  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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