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.

Physical Review LettersApr 20, 199257 citations

Journal of Statistical Physics

Precision calculation of elasticity for percolation

John G. Zabolitzky, David J. Bergman, Dietrich Stauffer

Published Jul 1, 1986• 94 citations

Publisher

DOI: 10.1007/bf01010913

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{T}_{\text{eb}}<{T}_{c}

at which the elastic backbone of FK clusters undergoes a second-order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, which leads us to propose a new anisotropic universality class with $\ensuremath{\beta}=0.54\ifmmode\pm\else\textpm\fi{}0.02$, ${\ensuremath{\nu}}_{||}=1.86\ifmmode\pm\else\textpm\fi{}0.01$, ${\ensuremath{\nu}}_{\ensuremath{\perp}}=1.21\ifmmode\pm\else\textpm\fi{}0.04$, and ${d}_{f}=1.53\ifmmode\pm\else\textpm\fi{}0.03$. All tested hyperscaling relations are shown to be valid.