Connectivity and the fracton dimension of percolation clusters

Abstract

The vibrational density of states of percolation clusters at threshold has been calculated for scalar models in two space dimensions. The effective fracton dimension is found to increase significantly with the spread of the short-range interactions. This is attributed to the gain in connectivity associated with an increased spread. Although the simulations do not ascertain the asymptotic scaling behavior, they are of direct relevance to experiments which are always performed on samples that are fractal over a limited range of scales. © 1990 Springer-Verlag.