Magnon-fracton crossover of the spin-wave density of states in the diluted two-dimensional ferromagnet.

Abstract

A numerical study of the spin-wave density of states on the infinite percolating cluster of the site diluted Heisenberg ferromagnet is presented. The Gaussian elimination algorithm is employed for the accurate determination of the integrated density of states as a function of concentration in large two-dimensional strips. At the percolation threshold the energy dependence of the density of states is \ensuremath{\rho}(E)\ensuremath{\propto}${E}^{\mathrm{\ensuremath{-}}\ensuremath{\varphi}}$. We obtained the value of \ensuremath{\varphi}=0.32\ifmmode\pm\else\textpm\fi{}0.02 consistent with the presence of fracton excitations at all length scales, in agreement with previous estimates. For concentrations above ${p}_{c}$ the density of states is constant in the magnon or long-wavelength regime while a crossover to the fracton regime occurs at shorter wavelengths. The magnon-fracton crossover in energy is smooth and no indication of a fracton-edge peak is found for this system.