Numerical verification of scaling for scattering from fractons

Abstract

The single-length-scale postulate for fractons and the scaling hypothesis for the dynamic structure factor are confirmed for scalar elasticity on bond-percolation clusters. The strain exponent \ensuremath{\sigma} is determined in two and three dimensions. Because of granularity and finite-size effects, these results cannot be obtained from site-percolation models for which the short-range structure fails to scale. Dipole-induced-dipole scattering is particularly sensitive to granularity.