Abstract
We examine the influence of spin-wave interactions on the properties of the Heisenberg ferromagnet in two dimensions, where long-range order is stabilized by anisotropy of easy-axis character. We find, in contrast to the behavior in three dimensions, the scattering amplitude for spin-wave--spin-wave interactions displays nonanalytic (logarithmic) behavior in the limit of long wavelengths. We examine the influence of this feature on the renormalization of the dispersion relation of long-wavelength spin waves. We also explore the influence of anisotropy on certain higher-order corrections examined earlier by Kosevich and Chubukov, for the isotropic limit of the two-dimensional Heisenberg model.
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