Estimates of Resistive and Conductive Exponents in Two
and Three Dimensions Using Extended Perimeter Method

Abstract

We use the `Extended Perimeter Method', to calculate the low density series in powers of p (where p is the probability) for the resistive and conductive susceptibilities. In the case of directed problem, the numerical analysis of the series based on the Pade' approximants techniques give the estimates of the critical exponents γ_C=0.87± 0.03 in two dimensions and γ_C=0.48± 0.02 in three dimensions for the first time. For undirected problem, we obtain only the series for resistive and conductive susceptibilities in three dimensions. On the basis of our analysis using non-defective approximants we estimate γ_R=2.83± 0.25, and γ_C=0.63± 0.07. We also remove the discrepancy in the 8th term of the series for χ_C(p) obtained by Fisch and Harris in 1978. We conclude that the 8th term is wrong due to a single error in the formula which was used in all dimensions.