Problem of Two Spin Deviations in a Linear Chain with Next-Nearest-Neighbor Interactions

The problem of two spin deviations from the fully aligned state is studied in a linear chain for the Hamiltonian [J(i,j) > 0]: $$\mathrm{H=-½}{\displaystyle \sum _{(\mathrm{nn})}}\mathrm{J(i,j)}{\mathbf{S}}_i·{\mathbf{S}}_j\mathrm{-½\alpha }{\displaystyle \sum _{(\mathrm{nnn})}}\mathrm{J(i,j)}{\mathbf{S}}_i·{\mathbf{S}}_j$$ , where (nn) and (nnn) mean nearest‐ and next‐nearest‐neighbor interactions, respectively. The behavior of the bound state, which is found to exist for α ≥ 0 only, is discussed.