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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 6, Pages 1404–1433 (Mi izv2098)  

This article is cited in 7 scientific papers (total in 7 papers)

The existence of lattice models with several types of pariticles

S. A. Pirogov


Abstract: In this paper we consider classical lattice models more general than those previously considered. We find conditions for them under which there exist $r$ different limiting ergodic Gibbs distributions.
Bibliography: 16 titles.

Full text: PDF file (2732 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:6, 1333–1357

Bibliographic databases:

UDC: 519.2
MSC: Primary 82A25; Secondary 60K35
Received: 26.03.1974

Citation: S. A. Pirogov, “The existence of lattice models with several types of pariticles”, Izv. Akad. Nauk SSSR Ser. Mat., 39:6 (1975), 1404–1433; Math. USSR-Izv., 9:6 (1975), 1333–1357

Citation in format AMSBIB
\Bibitem{Pir75}
\by S.~A.~Pirogov
\paper The existence of lattice models with several types of pariticles
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 6
\pages 1404--1433
\mathnet{http://mi.mathnet.ru/izv2098}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=403523}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 6
\pages 1333--1357
\crossref{https://doi.org/10.1070/IM1975v009n06ABEH001524}


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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. 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. V. M. Gercik, “Conditions for the nonuniqueness of the Gibbs state for lattice models having finite interaction potentials”, Math. USSR-Izv., 10:2 (1976), 429–443  mathnet  crossref  mathscinet  zmath
    3. D. Ruelle, “On manifolds of phase coexistence”, Theoret. and Math. Phys., 30:1 (1977), 24–29  mathnet  crossref  mathscinet
    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. Boguslaw Zegarliński, “Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures”, J Statist Phys, 43:3-4 (1986), 687  crossref  mathscinet  zmath
    6. S. A. Pirogov, “Coexistence of phases in a multicomponent lattice liquid with complex thermodynamic parameters”, Theoret. and Math. Phys., 66:2 (1986), 218–221  mathnet  crossref  mathscinet  isi
    7. 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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