Scaling approach to phonon-fracton crossover

A scaling approach is formulated for the vibrational modes, from phonon to fracton, of a fractal network. The ratio of fracton-to-phonon density of vibrational states at crossover is found to be noncritical, i.e., independent of the crossover length scale. A steplike increase in the density of states at crossover is justified by an appeal to the normalization requirement on a fractal network. Applications are made to different fractal models. Recent effective-medium-approximation results are shown to violate scaling.