Vibration properties of a percolating cluster

Abstract
We present for the first time a numerical study of the vibrational modes of a percolating cluster of mass points connected by elastic bonds. The density of states is characterized by a power law behaviour in the fracton frequency regime, while a transition to a Debye type spectrum occurs at lower frequencies. We also find that the fracton states are weakly localized with a wide range of localization lengths while the states in the low frequency regime are extended