VIBRATIONAL PROPERTIES OF RANDOM PERCOLATING NETWORKS

The vibrational density of states (DOS) of very large percolating clus ters (bond and site). is calculated in three dimensions using the spec tral moments method. It is confirmed that for site (bond) percolation, the slope of the DOS in the fracton regime is strongly dependent on t he occupation probability p and the particle interactions. For the bon d percolation, the DOS presents a more complex behaviour in the low-fr equency region than the Debye law observed in the site percolation. In teractions are represented by the Born Hamiltonian with first and seco nd nearest neighbours. Several models are studied: for each model, it is possible to define critical exponents. A comparison with experiment al results on silica aerogels is reported.