Effective-medium approximation for the dynamical excitations of percolating antiferromagnets

The dynamical-excitation spectrum of a diluted antiferromagnet is studied in the effective-medium approximation. Recent results based upon this approximation are revised and a detailed analysis of the structure factor for neutron scattering is carried out and evaluated numerically. The spectrum reveals a sharp crossover from extended to localized excitations at a crossover frequency, ${\omega }_c$∝(p-$p_c$ ${)}^{3/2}$, where p is the percolation concentration and $p_c$ is the percolation threshold of the diluted antiferromagnet. The results are compared with recent neutron-diffraction experiments and with the scaling model for fractons.