Power-law dependence on frequency of the Raman-scattering intensity of percolating networks

Large-scale simulations have been carried out for elucidating the power-law dependence on frequency of the Raman-scattering intensity $I_{\alpha \beta }\left(\omega \right)$ for $d=3\mathrm{}$ bond-percolating networks. We have used for this purpose a simple but powerful and accurate numerical method. Taking into account the dipole-induced-dipole mechanism, the clear evidence of the power-law dependence on frequency for $I_{\alpha \beta }\left(\omega \right)$ has been obtained above and below the phonon-fracton crossover frequency ${\omega }_c$. In addition, the profiles of the $\omega$ dependence for dynamical structure factor $S(\mathrm{q}, \omega )$ for $d=3\mathrm{}$ percolating networks are given for networks above the percolation threshold $p_c$. Physical interpretations for these results are given in a line with the dynamic scaling argument.