Geodesic
Infinite-range limit for correlation functions of lattice systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a lattice Fermi gas, the quantum and classical Heisenberg models, and the Ising model it is shown that in the limit of an interaction of infinite range the correlation functions of these systems are identical to the expressions for them obtained in the self-consistent field approximation. The Lebowitz–Penrose theorem is also proved by a modified method of N. N. Bogolyubov (Jr). It is shown in the Appendix that the number of interacting harmonics in the method of the approximating Hamiltonian admits any growth less than the growth of the volume of the system. 
@article{TMF_1984_61_1_a0,
     author = {L. A. Pastur and M. V. Shcherbina},
     title = {Infinite-range limit for correlation functions of lattice systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--16},
     year = {1984},
     volume = {61},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a0/}
}
TY  - JOUR
AU  - L. A. Pastur
AU  - M. V. Shcherbina
TI  - Infinite-range limit for correlation functions of lattice systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 3
EP  - 16
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a0/
LA  - ru
ID  - TMF_1984_61_1_a0
ER  - 
%0 Journal Article
%A L. A. Pastur
%A M. V. Shcherbina
%T Infinite-range limit for correlation functions of lattice systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 3-16
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a0/
%G ru
%F TMF_1984_61_1_a0
L. A. Pastur; M. V. Shcherbina. Infinite-range limit for correlation functions of lattice systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a0/

[1] Braut R., Fazovye perekhody, Mir, M., 1974

[2] Stenli G., Fazovye perekhody i kriticheskie yavleniya, Mir, M., 1979

[3] Van-Kampen N. G., Phys. Rev., 135:1 (1964), A362–A370 | DOI | MR

[4] Lebowitz J. L., Penrose O., J. Math. Phys., 7:1 (1966), 98–113 | DOI | MR | Zbl

[5] Hemmer P. C., Lebowitz J. L., “Systems with weak Long-range Potentials”, Phase Transitions and Critical Phenomena, eds. M. S. Green, C. Domb, Academic Press, N. Y., 1973 | MR

[6] Thompson C., Silver H., Commun. Math. Phys., 33:1 (1973), 53–60 | DOI | MR

[7] Bogolyubov N. N. (ml.), Metod issledovaniya modelnykh gamiltonianov, Nauka, M., 1974 | MR

[8] Bogolyubov N. N. (ml.), Brankov I. G., Zagrebnov V. A., Kurbatov A. M., Tonchev N. S., Metod approksimiruyuschego gamiltoniana v statisticheskoi fizike, Izd-vo BAN, Sofiya, 1981

[9] Kac M., Uhlenbeck G., Hemmer P., J. Math. Phys., 4:2 (1963), 216–228 ; 229–247 ; 5:1 (1964), 60–74 | DOI | MR | Zbl | Zbl | DOI | MR | Zbl

[10] Daison F., Montroll E., Kats M., Fisher M., Ustoichivost i fazovye perekhody, Mir, M., 1973 | MR

[11] Haymet A. D., Phys. Rev., B27:3 (1983), 1725–1731 | DOI | MR

[12] Kim I. H., Lee M. H., Phys. Rev., B24:7 (1981), 3961–3970 | DOI

[13] Rieckers A., Physica, 108A:1 (1981), 107–134 | DOI | MR

[14] Kamamyra H., Progr. Theor. Phys., 68:3 (1982), 764–780 | DOI

[15] Matsubara T., Matsuda H., Progr. Theor. Phys., 15:6 (1956), 569–582 | DOI

[16] Bogolyubov N. N. (ml.), O nekotorykh obobschennykh teoremakh v teorii modelnykh sistem, Preprint OIYaI D17-10418, OIYaI, Dubna, 1977