The existence of lattice models with several types of pariticles
Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1333-1357.

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

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.
@article{IM2_1975_9_6_a9,
     author = {S. A. Pirogov},
     title = {The existence of lattice models with several types of pariticles},
     journal = {Izvestiya. Mathematics },
     pages = {1333--1357},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a9/}
}
TY  - JOUR
AU  - S. A. Pirogov
TI  - The existence of lattice models with several types of pariticles
JO  - Izvestiya. Mathematics 
PY  - 1975
SP  - 1333
EP  - 1357
VL  - 9
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a9/
LA  - en
ID  - IM2_1975_9_6_a9
ER  - 
%0 Journal Article
%A S. A. Pirogov
%T The existence of lattice models with several types of pariticles
%J Izvestiya. Mathematics 
%D 1975
%P 1333-1357
%V 9
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a9/
%G en
%F IM2_1975_9_6_a9
S. A. Pirogov. The existence of lattice models with several types of pariticles. Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1333-1357. http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a9/

[1] Minlos R. A., Sinai Ya. G., “Yavlenie “razdeleniya faz” pri nizkikh temperaturakh v nekotorykh reshetchatykh modelyakh gaza, II”, Tr. Mosk. matem. ob-va, 19, 1968, 113–178 | MR

[2] Minlos R. A., Sinai Ya. G., “Novye rezultaty o fazovykh perekhodakh 1-go roda v modelyakh reshetochnogo gaza”, Tr. Mosk. matem. ob-va, 17, 1967, 213–242

[3] Dobrushin R. L., “Zadacha edinstvennosti gibbsovskogo sluchainogo polya i problema fazovykh perekhodov”, Funkts. analiz, 2:4 (1968), 44–57 | MR | Zbl

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

[5] Gertsik V. M., “Usloviya needinstvennosti gibbsovskogo sostoyaniya dlya reshetchatykh modelei s finitnym potentsialom vzaimodeistviya”, Uspekhi matem. nauk, 30:3 (1975), 159–160 | MR | Zbl

[6] Pirogov S. A., Sinai Ya. G., “Fazovye perekhody 1-go roda dlya malykh vozmuschenii modeli Izinga”, Funkts. analiz, 8:1 (1974), 25–31 | MR

[7] Pirogov S. A., “Fazovye perekhody 1-go roda dlya spinovykh modelei so spinom, prinimayuschim znacheniya $-1$, $0$, $1$”, Dokl. AN SSSR, 214:6 (1974), 1273–1275 | MR | Zbl

[8] Lanford O. E., Ruelle D., “Observables at infinity and states with short range correlation in statistical mechanics”, Comm. Math. Phys., 13 (1969), 194–215 | DOI | MR

[9] Ryuel D., Statisticheskaya mekhanika, strogie rezultaty, Mir, M., 1971

[10] Pierls R. E., “On model Ising's ferromagnetic”, Proc. Camb. Phil. Soc., 32 (1936), 477–481 | DOI

[11] Griffiths R. B., “Peierls proof of spontaneous magnetization in two-dimensional Ising ferromagnet”, Phys. Rev., A136 (1964), 437–439 | DOI | MR

[12] Dobrushin R. L., “Asimptoticheskoe povedenie gibbsovskikh sostoyanii dlya reshetchatykh sistem v zavisimosti ot formy sosuda”, Teoret. i matem. fizika, 12:1 (1972), 115–134

[13] Dobrushin R. L., “Existence of phase transition in models of a lattice gas”, Proc. Fifth Berk. Symp. Math. Stat. Prob., v. 3, 1967, 73–87

[14] Fisher M. E., Straley J. P., “Three-state Potts model and anomalous tneitieal points”, J. Phys. A: Math., Nucl. Gen., 6 (1973), 1310–1326 | DOI

[15] Ginibre J., Grossman A., Ruelle D., “Condensation of lattice gases”, Comm. Math. Phys., 3 (1969), 187–193 | DOI | MR

[16] Sinai Ya. G., Khelemskii A. Ya., “Opisanie differentsirovanii v algebrakh tipa algebr lokalnykh nablyudaemykh spinovykh sistem”, Funkts. analiz, 6:4 (1972), 99–100 | MR | Zbl