Long-wavelength anomalous diffusion mode in the two-dimensional XY dipole magnet

In a two-dimensional XY ferromagnet the dipole force induces a strong interaction between spin waves in the long-wavelength limit. The major effect of this interaction is the transformation of a propagating spin wave into a diffusion mode. We study the anomalous dynamics of such diffusion modes. We find that the Janssen-De Dominics functional, which governs this dynamics, approaches the non-Gaussian fixed point. A spin wave propagates by an anomalous anisotropic diffusion with the dispersion relation: iω~kΔyy and iω~kΔxx, where Δy=47/27 and Δx=47/36. The low-frequency response to the external magnetic field is found.