Missing modes in the density of states of fractal networks

Simulations on the vibrational density of states of very large percolation clusters are presented. Above threshold (p>${\mathit{p}}_{\mathit{c}}$), not only does one find no accumulation of modes around the phonon-fracton crossover, but the number of modes is also depressed throughout the fracton region. These ‘‘missing modes’’ accumulate near the upper frequency cutoff. The reason for this pileup is explained, and scaling considerations account for the dependence on p-${\mathit{p}}_{\mathit{c}}$ of the size of this effect.