Geodesic
Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 121-136 
A. G. Basuev. Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 121-136. http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a9/
@article{TMF_1984_58_1_a9,
     author = {A. G. Basuev},
     title = {Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {121--136},
     year = {1984},
     volume = {58},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a9/}
}
TY  - JOUR
AU  - A. G. Basuev
TI  - Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 121
EP  - 136
VL  - 58
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a9/
LA  - ru
ID  - TMF_1984_58_1_a9
ER  - 
%0 Journal Article
%A A. G. Basuev
%T Mayer expansions for gas of contours at low temperatures and in arbitrary external fields for the multicomponent ising model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 121-136
%V 58
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a9/
%G ru
%F TMF_1984_58_1_a9

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

Convergence of contour expansions is proved for $\operatorname{Re}\beta\ge\beta_1$ and arbitrary external fields. It is also shown that the cluster functions are holomorphic with respect to the external fields in regions in which the fields have constant sign. The results are based on the construction of uniform estimates for the considered expansions in the neighborhood of the physical region of variation of the external fields.

[1] Ryuell D., Statisticheskaya mekhanika, Mir, M., 1971, 367 pp.

[2] Pirogov S. A., Sinai Ya. G., TMF, 25:3 (1975), 358–369 ; 26:1 (1976), 61–76 | MR | MR

[3] Sinai Ya. G., Teoriya fazovykh perekhodov, Nauka, M., 1980, 208 pp. | MR

[4] Virchenko Yu. P., TMF, 52:3 (1982), 473–490 | MR

[5] Basuev A. G., TMF, 57:3 (1983), 338–353 | MR

[6] Peierls R., Proc. Cambridge Phil. Soc., 32:3 (1936), 477–481 | DOI | Zbl