Nonuniversal critical exponents for transport in percolating systems with a distribution of bond strengths

Abstract

Numerical simulations are used to examine the dependences of the percolation transport exponents on the distribution of bond strenghts g in two-dimensional models. We use the probability density function p(g)=$g^{\alpha }$, a case that arises naturally in percolation of continuum systems. Our results are consistent with earlier predictions that for 0<α<1 the exponent t¯ differs from its counterpart t in the standard discrete lattice percolation networks by (t¯-t)≊α/(1-α), while for α<0, the exponents t¯ and t are equal.