Geodesic
Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 120-126 Cet article a éte moissonné depuis la source Math-Net.Ru

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The two-magnon problem is solved for a chain of spins $s=1/2$ with allowance for the interaction of neighbors that come after the nearest neighbors. It is shown that for any interaetion of the second neighbors (all the interactions are ferromagnetic) a bound state of two spin waves exists for all $k$, $0 ($k$ is the center of mass momentum of the system of two magnons). For $k=\pi$ a sufficiently strong interaction of the second neighbors destroys the bound state, and this result eonfirms the results of [3, 4]. 
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     author = {I. G. Gochev},
     title = {Two-magnon states in a one-dimensional {Heisenberg} model with second-neighbor interaction},
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     pages = {120--126},
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I. G. Gochev. Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 120-126. http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/

[1] H. Bethe, Z. Physik, 71 (1931), 205 | DOI | Zbl

[2] M. Wortis, Phys. Rev., 132 (1963), 85 | DOI | MR

[3] C. Majumdar, J. Math. Phys., 10 (1969), 177 | DOI | MR

[4] I. Ono, S. Mikado, T. Oguchi, J. Phys. Soc. Japan, 30 (1971), 358 | DOI

[5] N. Fukuda, M. Wortis, J. Phys. Chem. Sol., 24 (1963), 1675 | DOI