Vibrational properties of random percolating networks

The vibrational density of states (DOS) of very large percolating clusters (bond and site). is calculated in three dimensions using the spectral moments method. It is confirmed that for site (bond) percolation, the slope of the DOS in the fracton regime is strongly dependent on the occupation probability p and the particle interactions. For the bond percolation, the DOS presents a more complex behaviour in the low-frequency region than the Debye law observed in the site percolation. Interactions are represented by the Born Hamiltonian with first and second nearest neighbours. Several models are studied: for each model, it is possible to define critical exponents. A comparison with experimental results on silica aerogels is reported.