Geodesic
Conditions for the nonuniqueness of the Gibbs state for lattice models having
Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 429-443.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1976_10_2_a11,
     author = {V. M. Gercik},
     title = {Conditions for the nonuniqueness of the {Gibbs} state for lattice models having},
     journal = {Izvestiya. Mathematics },
     pages = {429--443},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/}
}
TY  - JOUR
AU  - V. M. Gercik
TI  - Conditions for the nonuniqueness of the Gibbs state for lattice models having
JO  - Izvestiya. Mathematics 
PY  - 1976
SP  - 429
EP  - 443
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/
LA  - en
ID  - IM2_1976_10_2_a11
ER  - 
%0 Journal Article
%A V. M. Gercik
%T Conditions for the nonuniqueness of the Gibbs state for lattice models having
%J Izvestiya. Mathematics 
%D 1976
%P 429-443
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/
%G en
%F IM2_1976_10_2_a11
V. M. Gercik. Conditions for the nonuniqueness of the Gibbs state for lattice models having. Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 429-443. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/

[1] Griffiths R. B., “Peierls Proof of Spontaneous magnetization in a Two-Dimensional Ising Ferromagnet”, Phys. Rev., 136 A (1964), 437–439 | DOI | MR | Zbl

[2] Dobrushin R. L., “Suschestvovanie fazovogo perekhoda v dvumernoi i trekhmernoi modeli Izinga”, Teoriya veroyatn. i ee primen., 10 (1965), 209–230 | MR | Zbl

[3] Ginibre J., Grossman A., Ruelle D., “Condensation of Lattice Gases”, Commun. Math. Phys., 3 (1966), 187–193 | DOI | MR

[4] Berezin F. A., Sinai Ya. G., “Suschestvovanie fazovogo perekhoda dlya reshetchatogo gaza s prityazheniem mezhdu chastitsami”, Tr. Mosk. matem. ob-va, 17, 1967, 197–212 | MR

[5] Dobrushin R. L., “Existense of Phase Transitions in Models of Lattice Gas”, Symp. Math. Stat. Prob., v. 3 (Proc. V Berk.), 1967, 73–87

[6] Dobrushin R. L., “Zadacha edinstvennosti gibbsovskogo sluchainogo polya i problema fazovykh perekhodov”, Funkts. analiz, 2:4 (1968), 44–47 | MR

[7] Lebowitz J. L., Gallavotti G., “Phase Transitions in Binary Lattice Cases”, J. Math. Phys., 7 (1971), 1129–1133 | DOI

[8] Heilmann O. J., “Existense of Phase Transition in Certain Causes with Repulsive Potential”, Lett. al Nuovo Cimento, 3:3 (1972), 95–99 | DOI

[9] Heilmann O. J., Praestgaard E., “Phase Transition of Hard Hexagons on a Triangular Lattice”, J. Stat. Phys., 9:1 (1973), 23–44 | DOI

[10] Gertsik V. M., Dobrushin R. L., “Gibbsovskie sostoyaniya v reshetchatoi modeli s vzaimodeistviem na dva shaga”, Funkts. analiz, 8:3 (1974), 12–25 | MR | Zbl

[11] Pirogov S. A., “Sosuschestvovanie faz dlya reshetchatykh modelei s neskolkimi tipami chastits”, Izv. AN SSSR. Seriya matem., 39 (1975), 1404–1433 | MR

[12] Doob J. L., Stochastic Processes, N. Y., London, 1953 ; Дуб Д. Л., Вероятностные процессы, ИЛ, М., 1956 | MR | Zbl

[13] Dobrushin R. L., “Gibbsovskie sluchainye polya dlya reshetchatykh sistem s poparnym vzaimodeistviem”, Funkts. analiz, 2:4 (1968), 31–43 | MR

[14] Dobrushin R. L., “Gibbsovskie sluchainye polya. Obschii sluchai”, Funkts. analiz, 3:1 (1969), 27–35 | MR | Zbl

[15] Minlos R. A., Sinai Ya. G., “Novye rezultaty o fazovykh perekhodakh 1-go roda v modelyakh reshetchatogo gaza”, Tr. Mosk. matem. ob-va, XVII, 1967, 213–242

[16] Minlos R. A., Sinai Ya. G., “Yavlenie “razdeleniya faz” pri nizkikh temperaturakh v nekotorykh reshetchatykh modelyakh gaza. I”, Matem. sb., 73 (1967), 375–448 ; “II”, Тр. Моск. матем. об-ва, XIX, 1968, 113–178 | MR | MR