Conductivity exponents from the analysis of series expansions for random resistor networks

Abstract

There has been considerable controversy in recent years over the value of the conductivity exponent t. This exponent can be deduced from series expansions via the scaling relations, t= zeta +(d-2) nu , where zeta is deduced from differences between the exponents of the resistive ( gamma _r), percolative ( gamma _p) and conductive ( gamma _c) susceptibility. The author finds that allowance for non-analytic confluent corrections to scaling and the use of recent p_c estimates leads to estimates for gamma _r, gamma _p and gamma _c that are somewhat different to those of Fisch and Harris (1978); however, the differences between these exponents do not change significantly. Moreover the change in accepted estimates of nu in the last five years cancels some of this remaining discrepancy and she concludes (using the relation zeta = gamma _r- gamma _p), that t=1.31, d=2; t=2.04, d=3; t=2.39, d=4; t=2.72, d=5; with an error of about +or-0.10 in each case. The d=2 estimate is in significantly better agreement with those of other methods than that of Fisch and Harris.