The method of two-time Green's functions in the magnetism theory of metals with strong correlations
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 453-466 Cet article a éte moissonné depuis la source Math-Net.Ru

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We apply the Bogoliubov–Tyablikov method of two-time Green's functions to a multielectron theory of metals in the framework of the models with strong correlations, which are the Hubbard model and the Vonsovskii $s$$d(f)$ exchange model. We discuss the atomic representation in the problem of describing electron states, the metal–insulator transition, the problem of noncoherent states, and the Kondo effect. We analyze the ferromagnetism criterion in systems of strongly correlated electrons, which differs drastically from the Stoner condition.
Keywords: magnetism, Green's function, multielectron model, statistical physics.
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V. Yu. Irkhin. The method of two-time Green's functions in the magnetism theory of metals with strong correlations. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 453-466. http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a7/

[1] N. N. Bogolyubov, S. V. Tyablikov, Dokl. AN SSSR, 126:1 (1959), 53–56 ; Д. Н. Зубарев, УФН, 71:5 (1960), 71–116 ; В. Л. Бонч-Бруевич, С. В. Тябликов, Метод функций Грина в статистической механике, Физматлит, М., 1961 | MR | Zbl | DOI | MR | MR | Zbl

[2] S. V. Tyablikov, Metody kvantovoi teorii magnetizma, Nauka, M., 1975 | MR

[3] M. I. Auslender, V. Yu. Irkhin, J. Phys. C, 18:18 (1985), 3533–3545 | DOI

[4] Yu. A. Tserkovnikov, TMF, 7:2 (1971), 250–261 ; 49 (1981), 219–233 ; 50:2 (1982), 261–271 | DOI | DOI | MR | DOI | MR

[5] J. Hubbard, Proc. R. Soc. Lond. A, 276:1365 (1963), 238–257 | DOI

[6] J. Hubbard, Proc. R. Soc. Lond. A, 277:1369 (1964), 237–259 | DOI

[7] J. Hubbard, Proc. R. Soc. Lond. A, 281:1386 (1964), 401–419 | DOI

[8] J. Hubbard, Proc. R. Soc. Lond. A, 285:1403 (1965), 542–560 | DOI | MR

[9] V. Yu. Irkhin, Yu. P. Irkhin, Phys. Stat. Sol. (b), 183:1 (1994), 9–58 ; V. Yu. Irkhin, Phys. Metals Metallography, 110:7 (2010), 602–641, arXiv: 1103.5123 | DOI | DOI

[10] V. Yu. Irkhin, Yu. P. Irkhin, Elektronnaya struktura, fizicheskie svoistva i korrelyatsionnye effekty v $d$- i $f$-metallakh i ikh soedineniyakh, UrO RAN, Ekaterinburg, 2004

[11] A. O. Anokhin, V. Yu. Irkhin, Phys. Stat. Sol. (b), 165:1 (1991), 129–142 | DOI | MR

[12] A. O. Anokhin, V. Yu. Irkhin, M. I. Katsnelson, J. Phys.: Condens. Matter, 3:11 (1991), 1475–1491 | DOI

[13] V. V. Valkov, S. G. Ovchinnikov, TMF, 50:3 (1982), 466–476 | DOI | MR

[14] V. Yu. Irkhin, M. I. Katsnelson, J. Phys.: Condens. Matter, 2:34 (1990), 7151–7171 | DOI

[15] D. M. Edwards, J. A. Hertz, J. Phys. F: Metal Phys., 3:12 (1973), 2191–2205 | DOI

[16] V. Yu. Irkhin, M. I. Katsnelson, FMM, 66:1 (1988), 41–52

[17] V. Yu. Irkhin, A. V. Zarubin, Eur. Phys. J. B, 38:4 (2004), 563–570, arXiv: cond-mat/0103054 | DOI

[18] V. Yu. Irkhin, A. V. Zarubin, Phys. Rev. B, 70:3 (2004), 035116, 16 pp., arXiv: ; Solid State Phenomena, 168–169 (2011), 469–472 cond-mat/0212586 | DOI | DOI | MR

[19] A. Georges, G. Kotliar, W. Krauth, M. J. Rozenberg, Rev. Modern Phys., 68:1 (1996), 13–125 | DOI | MR

[20] M. I. Auslender, V. Yu. Irkhin, M. I. Katsnelson, J. Phys. C: Solid State Phys., 21 (1988), 5521 | DOI

[21] E. L. Nagaev, Fizika magnitnykh poluprovodnikov, Nauka, M., 1979

[22] J. Kondo, “Theory of dilute magnetic alloys”, Solid State Physics, 23, eds. F. Seitz, D. Turnbull, H. Ehrenreich, Academic Press, New York, 1969, 183–281 | DOI

[23] M. I. Katsnelson, V. Yu. Irkhin, L. Chioncel, A. I. Lichtenstein, R. A. de Groot, Rev. Mod. Phys., 80:2 (2008), 315–378, arXiv: 0711.0872 | DOI

[24] M. I. Auslender, V. Yu. Irkhin, M. I. Katsnelson, J. Phys. C: Solid State Phys., 17:4 (1984), 669–681 | DOI

[25] V. Yu. Irkhin, FMM, 64 (1987), 260–268