Long-wavelength anomalous diffusion mode in the two-dimensional XY dipole magnet
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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: i omega similar to k(y)(Delta y) and i omega similar to k(x)(Delta x), where Delta(y)=47/27 and Delta(x)=47/36. The low-frequency response to the external magnetic field is found.