Level statistics for vibrational eigenstates of percolation clusters

We show that the method of level statistics can be applied successfully to investigate the localization behavior of vibrations and spin-wave states on the infinite percolation cluster for p pc. The fluctuations of the density of states are well described within the framework of random matrix theory. We find that all excitations are localized for percolation clusters on the square lattice, including the so-called phonon (or magnon) states with low frequency (energy) and can conclude that the fracton–phonon crossover is not related to a localization–delocalization transition in d=2.