Geodesic
Stability of Gibbs distributions
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 296-302 
V. V. Krivolapova; G. I. Nazin. Stability of Gibbs distributions. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 296-302. http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a12/
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     author = {V. V. Krivolapova and G. I. Nazin},
     title = {Stability of {Gibbs} distributions},
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     year = {1985},
     volume = {65},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Lattice systems with binary interaction are considered. The Gibbs distributions characterizing the states of the systems are determined by generating functionals that satisfy Bogolyubov's equation. It is shown that to different regularity conditions of the Gibbs distributions there correspond different natures of the continuous dependence of the solutions of the Bogolyubov equation on the external field. This makes it possible to regard the regularity conditions as conditions of stability of the Gibbs distributions with respect to weak perturbations of them by external fields.

[1] Bogolyubov N. N., Izbr. tr., t. 2, Naukova dumka, Kiev, 1970 | MR

[2] Nazin G. I., DAN SSSR, 245:6 (1979), 1352–1355 | MR

[3] Glukhikh N. V., Nazin G. I., TMF, 38:3 (1979), 417–421

[4] Bogolyubov N. N., Izbr. tr., t. 3, Naukova dumka, Kiev, 1971 | MR

[5] Nazin G. I., II Mezhdunarodnyi simpozium po izbrannym problemam statisticheskoi mekhaniki, OIYaI, Dubna, 1981, 158–164

[6] Dobrushin R. L., Funkts. analiz i ego prilozh., 2:4 (1968), 31–43 | MR | Zbl

[7] Krivolapova V. V., Nazin G. I., TMF, 47:3 (1981), 362–374 | MR