Geodesic
Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg–Ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 1, pp. 129-148 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The link between Bogoiyubov's statistical variational principle for free energy, the method of partial diagram summation of the perturbation theory, and the Luttinger–Ward theorem is established. On the basis of Matsubara's Green's function method the nonlinear integral Dyson equation is solved by approximating the effective potential and a new implicit equation of magnetic state is obtained for the Ising model. 
@article{TMF_1970_2_1_a10,
     author = {Yu. G. Rudoi},
     title = {Bogolyubov's statistical variational principle and the {Green's} function method applied to the {Heisenberg{\textendash}Ising} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {129--148},
     year = {1970},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_1_a10/}
}
TY  - JOUR
AU  - Yu. G. Rudoi
TI  - Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg–Ising model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1970
SP  - 129
EP  - 148
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1970_2_1_a10/
LA  - ru
ID  - TMF_1970_2_1_a10
ER  - 
%0 Journal Article
%A Yu. G. Rudoi
%T Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg–Ising model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
%P 129-148
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1970_2_1_a10/
%G ru
%F TMF_1970_2_1_a10
Yu. G. Rudoi. Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg–Ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 1, pp. 129-148. http://geodesic.mathdoc.fr/item/TMF_1970_2_1_a10/

[1] S. V. Tyablikov, Metody kvantovoi teorii magnetizma, «Nauka», 1965 | MR

[2] T. Holstein, H. Primakoff, Phys. Rev., 58 (1940), 1098 | DOI | Zbl

[3] F. Dyson, Phys. Rev., 102 (1956), 1217 | DOI | MR | Zbl

[4] Yu. A. Izyumov, DAN SSSR, 125 (1959), 1227 | MR | Zbl

[5] D. ter Haar, Physica, 18 (1952), 199 | DOI | MR | Zbl

[6] F. Ferrari, C. C. Villi, Progr. Theor. Phys., 11 (1954), 328 | DOI | Zbl

[7] A. M. Guenault, D. C. MacDonald, Mol. Phys., 5 (1962), 525 | DOI | MR

[8] I. A. Kvasnikov, DAN SSSR, 110 (1956), 755

[9] I. A. Kvasnikov, Dissertatsiya, MIAN SSSR, 1956

[10] N. N. Bogolyubov, D. N. Zubarev, Yu. A. Tserkovnikov, DAN SSSR, 117 (1957), 788

[11] N. N. Bogolubov, Physica, 26, Proc. Utrecht Congress (1960), 1 | DOI

[12] M. D. Girardeau, J. Math. Phys., 3 (1962), 131 ; Phys. Rev., 140 (1965), A1139 | DOI | MR | DOI | MR

[13] V. V. Tolmachev, DAN SSSR, 134 (1960), 1324

[14] M. Gaudin, Nucl. Phys., 15 (1960), 89 ; C. Bloch, C. De Dominicis, Nucl. Phys., 7 (1958), 459 | DOI | MR | Zbl | DOI | Zbl

[15] S. V. Tyablikov, V. A. Moskalenko, DAN SSSR, 158 (1964), 839

[16] Yu. G. Rudoi, Vysokotemperaturnye razlozheniya v teorii ferromagnetizma, Preprint MIAN SSSR, 1964

[17] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Fizmatgiz, 1962 | MR | Zbl

[18] D. A. Kirzhnits, Polevye metody teorii mnogikh chastits, Atomizdat, 1963

[19] I. M. Ryzhik, I. S. Gradshtein, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, 1962 | MR

[20] G. W. Ford, G. E. Phlenbeck, Studies in Statist. Mech., 1, NHPC, Amst., 1962 | MR

[21] J. M. Luttinger, J. Ward, Phys. Rev., 118 (1960), 1417 | DOI | MR | Zbl

[22] A. Klein, Phys. Rev., 121 (1961), 950 | DOI | MR | Zbl

[23] C. Bloch, Studies in Statist. Mech., 3, NHPC, Amst., 1965

[24] Yu. G. Rudoi, DAN SSSR, 174 (1967), 316

[25] V. L. Bonch-Bruevich, ZhETF, 30 (1956), 342; ФТТ, 4 (1957), 546; 6 (1958), 590

[26] J. Hubbard, Proc. Roy. Soc., A240 (1957), 539 ; Вопросы квантовой теории многих тел, Сб., ИЛ, 1959 | DOI | MR | Zbl

[27] C. Bloch, J. S. Langer, J. Math. Phys., 6 (1965), 554 | DOI | MR

[28] V. G. Vaks, A. I. Larkin, S. A. Pikin, ZhETF, 51 (1966), 361; 53 (1967), 291

[29] R. Brout, Phys. Rev., 118 (1960), 1009 ; 122 (1961), 469 | DOI | MR | Zbl | DOI | MR

[30] T. H. Berlin, M. Kac, Phys. Rev., 86 (1952), 821 | DOI | MR | Zbl

[31] G. N. Watson, Quart. J. Math., 10 (1939), 266 | DOI | Zbl

[32] M. Lax, Phys. Rev., 97 (1956), 629 | DOI | MR

[33] M. Wortis, Phys. Rev., 138 (1965), 1126 | DOI | MR

[34] L. D. Kadanov, G. Beim, Kvantovaya statisticheskaya mekhanika, «Mir», 1964

[35] J. Czerwonko, Acta phys. polon., 22 (1962), 445 | MR

[36] V. Ya. Krivnov, Dissertatsiya, MFTI, 1969