Estimates of Resistive and Conductive Exponents in Two and Three Dimensions Using Extended Perimeter Method - Faqir M. Bhatti, (The Physical Society of Japan, 2000)
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 gamma (C) = 0.87 +/- 0.03 in two dimensions and gamma (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 gamma (R) = 2.83 +/- 0.25, and gamma (C) = 0.63 +/- 0.07. We also remove the discrepancy in the 8th term of the series for chi (C)(p) obtained hy 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.