Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet

Abstract

In 2D 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: $iω{\sim}k_{y}^{Δ_y}$ and $iω{\sim}k_{x}^{Δ_x}$, where ${Δ_y}=47/27$ and ${Δ_x}=47/36$. The low-frequency response to the external magnetic field is found.