Abstract
The -dimensional bond-percolating network has been examined with the use of the effective-medium approximation (EMA) of Odagaki and Lax and of Webman. We have found that the fracton dimensionality for , and have obtained explicit values for between . We have calculated the vibrational density of states, , for percolating networks within the EMA for in these ranges. We find at that a steep change in takes place between phonon, , and fracton, , excitation regimes at a critical frequency which scales as . The ratio is found to scale as . These results provide substantial support for the fracton interpretation of the thermal properties of epoxy resin, glasses, and neutron-irradiated quartz as hypothesized by Alexander, Laermans, Orbach, and Rosenberg. At , the transition between the two regimes is smoother (logarithmic), but a clearly defined phonon and fracton regime can be ascertained. The velocity of sound in the phonon regime scales as , independent of for . Finally, we have obtained within the EMA a closed expression for the mean-square diffusion length for all times of order . It is found to be a smooth function of time between the fractal and homogeneous diffusion regimes.
- Received 21 September 1983
DOI:https://doi.org/10.1103/PhysRevB.29.6645
©1984 American Physical Society