Critical indexes of conductivity in two-dimensional percolation problems

Abstract

The results of model experiments for critical behaviour of conductivity in two-dimensional percolation problems are presented. It is found that for the system consisting of conductive and non-conductive elements conductivity vanishes as sigma (x) infinity (xc-x)t; where t is equal to 1.15+or-0.2 for both bond and site percolation problems. For the two-component system consisting of metallic and dielectric elements it is found that if the fraction of the dielectric phase x with the conductivity sigma D tends to the percolation threshold xc above, the conductivity of the system increases as sigma (x)= sigma D(x-xc)-q, where q is a new critical index. The value q=t=1.15+or-0.25 is obtained in agreement with the prediction of Efros and Shklovskii (1976).