Geodesic
Spectrum of the energy operator of two-magnon systems in the isotropic Heisenberg ferromagnet model with impurity
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 464-472 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a two-magnon system in the isotropic Heisenberg ferromagnet model with impurity on a $\nu$-dimensional lattice $\mathbb Z^{\nu}$. We establish that the essential spectrum of the system consists of the union of at most four intervals. We obtain the lower and upper estimates for the number of three-particle bound states of the system.
Keywords: essential spectrum, discrete spectrum, local impurity state, bound state, Heisenberg model, two-magnon system in the impurity model. 
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     title = {Spectrum of the~energy operator of two-magnon systems in the~isotropic {Heisenberg} ferromagnet model with impurity},
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S. M. Tashpulatov. Spectrum of the energy operator of two-magnon systems in the isotropic Heisenberg ferromagnet model with impurity. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 464-472. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a16/

[1] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 3, Mir, M., 1982 | MR | MR | Zbl

[2] S. M. Tashpulatov, TMF, 126:3 (2001), 482–488 | DOI | MR | Zbl

[3] M. A. Naimark, Normirovannye koltsa, Nauka, M., 1968 | MR | MR | Zbl

[4] M. Wortis, Phys. Rev., 132:1 (1963), 85–97 | DOI | MR

[5] S. M. Tashpulatov, TMF, 107:1 (1996), 155–161 | DOI | MR | Zbl

[6] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 1, Funktsionalnyi analiz, Mir, M., 1977 | MR | MR | Zbl

[7] T. Ichinose, Trans. Amer. Math. Soc., 235 (1978), 75–113 | DOI | MR | Zbl

[8] T. Ichinose, Trans. Amer. Math. Soc., 237 (1978), 223–254 | DOI | MR | Zbl

[9] T. Ichinose, “On the spectral properties of tensor products of linear operators in Banach spaces”, Spectral Theory, Banach Center Publ., 8, eds. W. Żelazko, PWN, Warsaw, 1982, 294–300 | MR | Zbl

[10] S. M. Tashpulatov, TMF, 162:2 (2010), 227–242 | DOI | MR | Zbl