A novel determination of the percolation exponent u in three dimensions

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Abstract
The authors present an accurate determination of the percolation transport exponent u=t/(s+t) in three dimensions, based on a transfer-matrix approach to the AC (frequency-dependent) conductivity, and a finite-size scaling analysis of the numerical data. The phase of the complex conductivity, the loss angle, assumes the universal value delta c=( pi /2)(1-u) at low frequency at the percolation threshold. As a test of their numerical scheme, the two-dimensional exact duality result delta c= pi /4 (i.e. s=t) is recovered with a very good accuracy. In three dimensions, their data are extrapolated to tan delta c=0.54+or-0.03, i.e. u=0.69+or-0.02, whereas the usually accepted values s/v=0.85+or-0.04, t/v=2.2+or-0.1 yield u=0.72+or-0.02. This marginal disagreement can be attributed to ill behaved corrections to finite-size scaling.