RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1468 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.2
MSC: 82A40

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} 

• http://mi.mathnet.ru/eng/izv2119
• http://mi.mathnet.ru/eng/izv/v40/i2/p448

 SHARE:

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
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
3. D. G. Martirosyan, “Uniqueness of Gibbs states in lattice models with one ground state”, Theoret. and Math. Phys., 63:2 (1985), 511–518
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
5. Eugene Pechersky, Elena Petrova, Sergey Pirogov, “Phase transitions of laminated models at any temperature”, Mosc. Math. J., 10:4 (2010), 789–806
•  Number of views: This page: 168 Full text: 43 References: 31 First page: 1