  We study the magnetic excitation spectrum in three-dimensional diluted
ferromagnetic nearest-neighbor systems down to the percolation threshold. The
disorder effects resulting from the dilution are handled accurately within
self-consistent local random phase approximation approach. The calculations are
performed using relatively large systems containing typically 20 000 localized
spins, a systematic average over many configurations of disorder is performed.
We analyze in details the change in the magnon spectrum and magnon density of
states as we increase the dilution. The zone of stability of the well-defined
magnon modes is shown to shrink drastically as we approach the percolation
threshold. We also calculate the spin stiffness which appears to vanish at the
percolation threshold exactly. A comparison with available data, based on a
different theoretical approach, is also provided. We hope that this study will
motivate new experimental studies based on inelastic neutron-scattering
measurements.
