Geodesic
Spectrum of Two-Magnon non-Heisenberg Ferromagnetic Model of Arbitrary Spin with Impurity
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 2, pp. 239-265 
S. M. Tashpulatov. Spectrum of Two-Magnon non-Heisenberg Ferromagnetic Model of Arbitrary Spin with Impurity. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 2, pp. 239-265. http://geodesic.mathdoc.fr/item/JMAG_2013_9_2_a6/
@article{JMAG_2013_9_2_a6,
     author = {S. M. Tashpulatov},
     title = {Spectrum of {Two-Magnon} {non-Heisenberg} {Ferromagnetic} {Model} of {Arbitrary} {Spin} with {Impurity}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {239--265},
     year = {2013},
     volume = {9},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_2_a6/}
}
TY  - JOUR
AU  - S. M. Tashpulatov
TI  - Spectrum of Two-Magnon non-Heisenberg Ferromagnetic Model of Arbitrary Spin with Impurity
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2013
SP  - 239
EP  - 265
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JMAG_2013_9_2_a6/
LA  - en
ID  - JMAG_2013_9_2_a6
ER  - 
%0 Journal Article
%A S. M. Tashpulatov
%T Spectrum of Two-Magnon non-Heisenberg Ferromagnetic Model of Arbitrary Spin with Impurity
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2013
%P 239-265
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2013_9_2_a6/
%G en
%F JMAG_2013_9_2_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a two-magnon system in the isotropic non-Heisenberg ferromagnetic model of an arbitrary spin $s$ on a $\nu$-dimensional lattice $Z^{\nu}$. We establish that the essential spectrum of the system consists of the union of at most four intervals. We obtain lower and upper estimates for the number of three-particle bound states, i.e., for the number of points of discrete spectrum of the system.

[1] S. M. Tashpulatov, “One-Magnon Systems in an Isotropic non-Heisenberg Ferromagnetic Impurity Model”, Theor. Math. Phys., 142:1 (2005), 83–92 | DOI | MR | Zbl

[2] M. Reed, B. Simon, Methods of Modern Mathematical Physics, v. 1, Funct. Anal., Acad. Press, New York, 1977 | MR | Zbl

[3] V. V. Val'kov, S. G. Ovchinnikov, O. P. Petrakovskii, “Spectra of Two-Magnon System Excitations in the Easy Axis Quasidimensional Ferromagnetics”, Fiz. Tverd. Tela, 30 (1988), 3044–3047

[4] S. M. Tashpulatov, “Spectra and Bound States of the Energy Operator of Two-Magnon Systems in a Isotropic non-Heisenberg Ferromagnet with Nearest-Neighbour Interactions and Arbitrary Spin Value $S$”, Uzbek. Math. J., 2008, no. 1, 95–111 | MR | Zbl

[5] Wolters-Noordhoff, Graningen, 1970 | MR

[6] T. Ichinose, “Spectral Properties of Tensor Products of Linear Operators, 1”, Trans. Amer. Math. Soc., 235 (1978), 75–113 | DOI | MR | Zbl

[7] T. Ichinose, “Spectral Properties of Tensor Products of Linear Operators. 2: The Approximate Point Spectrum and Kato Essential Spectrum”, Trans. Amer. Math. Soc., 237 (1978), 223–254 | MR | Zbl

[8] T. Ichinose, “On the spectral properties of tensor products of linear operators in Banach spaces”, Banach Center Publications, 8, no. 1, PWN-Polish Scientific Publishers, Warsaw, 1982, 295–300 | MR

[9] H. Hochstadt, “One Dimensional Perturbations of Compact Operators”, Proc. Amer. Soc., 37 (1973), 465–467 | DOI | MR | Zbl

[10] H. Vasueda, “One Dimensional Perturbations of Compact Operators”, Proc. Amer. Soc., 57:1 (1976), 58–60 | DOI | MR

[11] S. V. Shevchenko, “About Dependence of Spectral Properties of Matrix to Relative of Perturbation with Sufficiently Low Ranks”, Funct. Anal. Appl., 38:1 (2004), 85–88 | MR