Electrical conductivity of finite-size percolation networks

Abstract

Calculating, by a Monte Carlo technique, the conductivities of small, two-dimensional, square, bond-percolation networks (4*4 to 50*50) at a limited number of probability values, from the critical region to full conductivity, the authors have been able to show, by an original interpolation technique, that in the critical region the conductivity function does indeed obey a universal, Fisher-type, finite-size scaling function. They further show that this technique permits them to deduce values of the critical exponents for both the conductivity and the correlation length, even from calculations on relatively small networks.