Monte Carlo experiment for the two-dimensional site percolation network

Abstract

A Monte Carlo computer experiment gives the bulk conductivity of a 200*200 site square resistor network consisting of two kinds of unit resistor with difference conductance. An enumeration of clusters of one phase in the networks with 200*200 sites and 500*500 sites provides the percolation probability and an estimate of the critical probability 0.59<Pc<<0.60 for the square site system. The critical conductivity exponent is reported to be t=1.26+or-0.03 for the critical percolation probability pc=0.591+or-0.001. The critical exponent of the percolation probability is found to be s=0.20+or-0.03 for the square site system.