Geodesic
Tensor of the inhomogeneous dynamic susceptibility of an anisotropic Heisenberg ferromagnet and Bogolyubov inequalities. I. Single-particle matrix Green's function and transverse components of the susceptibility tensor
Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 101-114 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two-time thermal Green's functions are used to consider the tensor of the inhomogeneous dynamic susceptibility $\chi^{\alpha\beta}(k,E)$ of the generalized anisotropic three-dimensional Heisenberg model with spin $1/2$. The transverse components ($\alpha,\beta=x,y$) are obtained by means of the single-particle matrix Green's function in the generalized Hartree–Fock approximation. The Tyablikov approximation is used to analyze the dependence of the diagonal components $\chi^x_k$ and $\chi^y_k$ in the static limit $E=0$ on the quasimomentum, the anisotropy, and the external field in a wide range of temperatures. It is shown in particular that for degenerate models of the easy plane type (including the isotropic case) which in the absence of a field have a gapless spectrum one or both of the components $\chi^x_k$ and $\chi^y_k$ diverge at $k=0$ in the ferromagnetic region, while in the paramagnetic region they have the Ornstein–Zernike form. The obtained results are in agreement with Bogolyubov's rigorous inequalities, which are generalized to the case of arbitrary anisotropy. 
@article{TMF_1979_38_1_a9,
     author = {Yu. G. Rudoi},
     title = {Tensor of the inhomogeneous dynamic susceptibility of an anisotropic {Heisenberg} ferromagnet and {Bogolyubov} {inequalities.~I.} {Single-particle} matrix {Green's} function and transverse components of the susceptibility tensor},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {101--114},
     year = {1979},
     volume = {38},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a9/}
}
TY  - JOUR
AU  - Yu. G. Rudoi
TI  - Tensor of the inhomogeneous dynamic susceptibility of an anisotropic Heisenberg ferromagnet and Bogolyubov inequalities. I. Single-particle matrix Green's function and transverse components of the susceptibility tensor
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 101
EP  - 114
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a9/
LA  - ru
ID  - TMF_1979_38_1_a9
ER  - 
%0 Journal Article
%A Yu. G. Rudoi
%T Tensor of the inhomogeneous dynamic susceptibility of an anisotropic Heisenberg ferromagnet and Bogolyubov inequalities. I. Single-particle matrix Green's function and transverse components of the susceptibility tensor
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 101-114
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a9/
%G ru
%F TMF_1979_38_1_a9
Yu. G. Rudoi. Tensor of the inhomogeneous dynamic susceptibility of an anisotropic Heisenberg ferromagnet and Bogolyubov inequalities. I. Single-particle matrix Green's function and transverse components of the susceptibility tensor. Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 101-114. http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a9/

[1] Yu. G. Rudoi, Yu. A. Tserkovnikov, TMF, 14 (1973), 102

[2] Yu. G. Rudoi, Yu. A. Tserkovnikov, TMF, 19 (1974), 19

[3] Yu. G. Rudoi, Yu. A. Tserkovnikov, “Prilozheniya metoda funktsii Grina k teorii anizotropnykh geizenbergovskikh ferro- i antiferromagnetikov”, gl. 1–3, Dopolneniya k monografii { [4]}

[4] S. V. Tyablikov, Metody kvantovoi teorii magnetizma, izd. 2-e, «Nauka», 1975 | MR

[5] N. N. Bogolyubov, Preprint OIYaI D-781, Dubna, 1961; Избр. труды, т. 3, «Наукова думка», 1971 | MR

[6] N. N. Bogolyubov (ml.), B. I. Sadovnikov, Nekotorye voprosy statisticheskoi mekhaniki, «Vysshaya shkola», 1975 | MR

[7] A. Z. Patashinskii, V. L. Pokrovskii, Fluktuatsionnaya teoriya fazovykh perekhodov, «Nauka», 1975 ; ЖЭТФ, 64 (1973), 1445 | MR

[8] A. Isikhara, Statisticheskaya fizika, «Mir», 1973 | MR

[9] V. P. Kalashnikov, Preprint OIYaI R4-7803, Dubna, 1974 | Zbl

[10] J. Goldstone, Nuovo Cim., 19 (1961), 154 | DOI | MR | Zbl

[11] G. Stenli, Fazovye perekhody i kriticheskie yavleniya, «Mir», 1973

[12] Yu. G. Rudoi, TMF, 26 (1976), 387

[13] K. Kawasaki, H. Mori, Progr. Theor. Phys., 28 (1962), 690 | DOI | MR | Zbl

[14] Yu. G. Rudoi, Yu. A. Tserkovnikov, TMF, 25 (1975), 196

[15] H. Wagner, Z. Phys., 195 (1966), 273 | DOI

[16] B. I. Sadovnikov, V. K. Fedyanin, TMF, 16 (1973), 368 | MR

[17] V. K. Fedyanin, FMM, 28 (1969), 117

[18] H. B. Callen, Phys. Rev., 130 (1963), 890 | DOI | Zbl

[19] H. Hugenholtz, D. Pines, Phys. Rev., 116 (1959), 489 | DOI | MR | Zbl

[20] Yu. A. Tserkovnikov, DAN SSSR, 143 (1962), 832 ; Статистическая физика и квантовая теория поля, Сб., ред. Н. Н. Боголюбов, «Наука», 1973 | Zbl | MR