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\ensuremath{\propto}(p-${p}_{c}$${)}^{t}$ and S\ensuremath{\propto}(p-${p}_{c}$${)}^{f}$, with t=1.24\ifmmode\pm\else\textpm\fi{}0.13, in agreement with the value for lattice percolation, and f=4.95\ifmmode\pm\else\textpm\fi{}1.1, which differs from the lattice value. These results are in excellent agreement with recent scaling predictions.