Measurement of nonuniversal critical behavior in a two-dimensional continuum percolating system

Abstract

We report the results of measurements of the stiffness S and conductance G of square metal sheets as a function of the number of randomly drilled holes or, equivalently, the area fraction of metal p. The data near p=1 are well described by effective-medium theory: G(p)=2G(1)(p-(1/2)) and S(p)=3S(1)(p-(2/3)). Near the percolation threshold, $p_c$, we find that G∝(p-$p_c$ ${)}^t$ and S∝(p-$p_c$ ${)}^f$, with t=1.24±0.13, in agreement with the value for lattice percolation, and f=4.95±1.1, which differs from the lattice value. These results are in excellent agreement with recent scaling predictions.