SPECTRUM OF EXCITATIONS OF A DISORDERED A'XA''1-XB CRYSTAL WITH AN ISOTOPIC IMPURITY CONCENTRATION CLOSE TO THE PERCOLATION-THRESHOLD

The renormalization group method is used to calculate the average one- particle Green's function of a cubic diatomic crystal containing an is otopic impurity under conditions close to the percolation threshold. I t is shown that in the case of long-wavelength excitations there are t wo characteristic frequencies of the optical and acoustic branches of the spectrum, respectively, which separate the phonon and fracton regi mes. The critical exponent which describes the density of states, the phonon retardation effect, and the frequency dependence of the average size of a fracton excitation, is calculated.