Geodesic
Effective spin Hamiltonian and phase separation in the almost half-filled Hubbard model and the narrow-band $s$-$f$ model
Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 436-444 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An effective Hamiltonian of the spin degrees of freedom in the almost half-filled Hubbard model is constructed by means of functional integration in the static approximation. It is shown that in the narrow-band case formal perturbation theory in the ratio of the band width to the Coulomb repulsion coupling constant leads to terms which diverge as the temperature tends to zero. To remove these divergences, the so-called Cayley-tree approximation is used. In this approximation, in the leading orders in the small parameter an effective spin Hamiltonian of the model is derived. In a certain range of variation of the electron density, this Hamiltonian describes a separation of the system into a conducting ferromagnetic phase and a dielectric antiferromagnetic phase. It is shown that the interphase boundary has a thickness of the order of the lattice constant. It is also established that there is a connection between the narrow-band Hubbard model and the narrow-band $s$-$f$ model. 
@article{TMF_1982_51_3_a13,
     author = {M. I. Auslender and M. I. Katsnel'son},
     title = {Effective spin {Hamiltonian} and phase separation in the almost half-filled {Hubbard} model and the narrow-band $s$-$f$ model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {436--444},
     year = {1982},
     volume = {51},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a13/}
}
TY  - JOUR
AU  - M. I. Auslender
AU  - M. I. Katsnel'son
TI  - Effective spin Hamiltonian and phase separation in the almost half-filled Hubbard model and the narrow-band $s$-$f$ model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1982
SP  - 436
EP  - 444
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a13/
LA  - ru
ID  - TMF_1982_51_3_a13
ER  - 
%0 Journal Article
%A M. I. Auslender
%A M. I. Katsnel'son
%T Effective spin Hamiltonian and phase separation in the almost half-filled Hubbard model and the narrow-band $s$-$f$ model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1982
%P 436-444
%V 51
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a13/
%G ru
%F TMF_1982_51_3_a13
M. I. Auslender; M. I. Katsnel'son. Effective spin Hamiltonian and phase separation in the almost half-filled Hubbard model and the narrow-band $s$-$f$ model. Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 436-444. http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a13/

[1] Nagaev E. L., Fizika magnitnykh poluprovodnikov, Nauka, M., 1979, 432 pp.

[2] Khomskii D. I., FMM, 29:1 (1970), 31–57

[3] Nagaoka Y., Phys. Rev., 147:1 (1966), 392–405 | DOI

[4] Brinkman W. F., Rice T. M., Phys. Rev., B2:5 (1970), 1324–1338 | DOI

[5] Visscher P. B., Phys. Rev., B10:3 (1974), 932–942 ; 943–946 | DOI | MR

[6] Zaitsev R. O., FTT, 19:11 (1977), 3204–3213

[7] Nagaev E. L., “Silnolegirovannye magnitnye poluprovodniki”, Redkozemelnye poluprovodniki, Sb., Nauka, L., 1977, 48–81

[8] Erukhimov M. Sh., Sandalov I. S., FTT, 19:8 (1977), 1377–1385

[9] Moriya T., JMMM, 14:1 (1979), 1–46 | DOI

[10] Morandi G., Galleani d'Agliano E., Napoli F., Ratto C. F., Adv. Phys., 23:6 (1974), 867–916 | DOI

[11] Castellani C., Di Castro C., Feinberg D., Ranninger J., Phys. Rev. Lett., 43:26 (1979), 1957–1960 | DOI

[12] Abou-Chacra R., Anderson P. W., Thouless D. J., J. Phys., C6:10 (1973), 1734–1752

[13] Elyutin P. V., FTT, 21 (1979), 2765–2771 | MR

[14] Anderson P. W., Phys. Rev., 83:6 (1951), 1260–1271 | DOI

[15] Anderson P. W., “Theory of magnetic exchange interactions: exchange in insulators and semiconductors”, Solid State Physics, 14, ed. Turnbull D., Seitz F., Academic Press, N. Y., 1963, 99–214 | DOI