Bound States of Two Spin Waves in the Heisenberg Ferromagnet

The simple cubic nearest-neighbor Heisenberg model is discussed in one, two, and three dimensions for arbitrary spin. The problem of two spin deviations propagating in an otherwise fully aligned lattice is reduced to quadratures. The integrals relevant to the bound-state problem are examined. It is found that bound states exist for all spins and dimensionalities. In one dimension the results of Bethe and others are reaffirmed. In two and three dimensions the total momentum of a bound pair determines the number of possible bound states. For positive exchange constant and sufficiently large longitudinal anisotropy there are bound states of two spin waves with energies below all continuum energies. It is argued that these states should have a dominant influence on the low-temperature thermodynamics.

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