Monte Carlo evidence against the Alexander-Orbach conjecture for percolation conductivity

Abstract

The conductivity of a random network of resistors and insulators in two dimensions is calculated for strips of size $N\times L$ with $L$ of the order of several ${10}^6$ and $N$ up to 350. At the percolation threshold I find the finite-size conductivity exponent $\frac{t}{\nu }$ to be 0.973±0.005 in contradiction to the Alexander-Orbach conjecture $\frac{t}{\nu }\approx 0.948$ and also incompatible with $\frac{t}{\nu }=1.0\mathrm{}$.