Geodesic
Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume
Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 1, pp. 115-134
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A study is made of the cases for which the existence of Gibbsian states in an infinite lattice was proved in earlier papers. It is proved that Gibbstan states exist in an infinite region, which may be part of the complete lattice, and an investigation is made of the dependence of the correlation functions on the form of the region. The second term in the asymptotic behavior of the free energy, which depends on the form of the region, is found. Finally, some properties of correlation weakening for such Gibbsian states are investigated. 
@article{TMF_1972_12_1_a10,
     author = {R. L. Dobrushin},
     title = {Asymptotic behavior of {Gibbsian} distributions for lattice systems and its dependence on the form of the volume},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {115--134},
     year = {1972},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a10/}
}
TY  - JOUR
AU  - R. L. Dobrushin
TI  - Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1972
SP  - 115
EP  - 134
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a10/
LA  - ru
ID  - TMF_1972_12_1_a10
ER  - 
%0 Journal Article
%A R. L. Dobrushin
%T Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1972
%P 115-134
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a10/
%G ru
%F TMF_1972_12_1_a10
R. L. Dobrushin. Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume. Teoretičeskaâ i matematičeskaâ fizika, Tome 12 (1972) no. 1, pp. 115-134. http://geodesic.mathdoc.fr/item/TMF_1972_12_1_a10/

[1] D. Ruelle, Statistical mechanics. Rigorous results, N.-Y.–Amsterdam, 1969 ; D. Ryuel, Statisticheskaya mekhanika. Strogie rezultaty, «Mir», 1971 | MR

[2] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 2 (1968), 44 | Zbl

[3] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 2 (1968), 31 | Zbl

[4] O. E. Lanford III, D. Ruelle, Commun. Math. Phys., 13 (1968), 194 | DOI | MR

[5] I. A. Ibragimov, Yu. L. Rozanov, Gaussovskie sluchainye protsessy, «Nauka», 1970 | MR

[6] R. A. Minlos, Funktsionalnyi analiz i ego prilozheniya, 1 (1967), 40 | MR | Zbl

[7] R. A. Minlos, Ya. G. Sinai, Trudy Moskovskogo matematicheskogo obschestva, 17 (1967), 213

[8] R. A. Minlos, Ya. G. Sinai, Trudy Moskovskogo matematicheskogo obschestva, 19 (1968), 113 | MR

[9] R. L. Dobrushin, Teoriya veroyatnostei i ee primeneniya, 15 (1970), 469 | Zbl

[10] R. L. Dobrushin, Proc. Fifth. Berkeley Symp. on Math. Stat. and Prob., 3, 1968, 73

[11] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 3 (1969), 27 | Zbl

[12] Dzh. Dub, Veroyatnostnye protsessy, IL, 1956 | MR

[13] R. L. Dobrushin, Teoriya veroyatnostei i ee primeneniya, 13 (1968), 201

[14] R. L. Dobrushin, Teoriya veroyatnostei i ee primeneniya, 10 (1965), 209 | MR | Zbl

[15] I. L. Lebowitz, An. Rev. Phys. Chem., 19 (1968), 389 | DOI