Critical exponents of percolating wire networks

Abstract

Measurements of electronic and magnetic properties of percolating, aluminum wire networks are presented and compared with numerical and analytic results. As opposed to vapor-deposited films, these networks are well suited for comparison to theory of two-dimensional percolation since they are exact replicas of models used to study percolation. We find that the ratio of the exponents for the conductivity and the percolation length, $\frac{t}{\nu }=0.98\mathrm{}\pm 0.03$, is consistent with recent computer studies but not with the Alexander-Orbach conjecture. The critical current exponent, within error, is given by $v=\nu =\frac{4}{3}$. Finally, the critical field exponent is given by $k=1.11\mathrm{}\pm 0.04$, consistent with our prediction of $k=\nu \Theta \sim 1.15$ as well as with numerical studies.