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

TL;DR

This paper investigates the anomalous diffusion modes in 2D XY ferromagnets caused by dipole interactions, revealing non-Gaussian fixed points and anisotropic dispersion relations for spin-waves.

Contribution

It introduces a detailed analysis of the long-wavelength spin-wave dynamics, showing the transformation into diffusion modes with specific anisotropic exponents and fixed-point behavior.

Findings

Spin-waves exhibit anisotropic anomalous diffusion with specific exponents.

The dynamics approach a non-Gaussian fixed point.

Low-frequency magnetic response characterized.

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: $i\omega{\sim}k_{y}^{\Delta_y}$ and $i\omega{\sim}k_{x}^{\Delta_x}$, where ${\Delta_y}=47/27$ and ${\Delta_x}=47/36$. The low-frequency response to the external magnetic field is found.