Percolative conduction in three dimensions

We employ finite-size scaling to analyze the critical behavior of large [up to (80${)}^3$] three-dimensional random resistor lattices. The ratio of the conductivity exponent t to the correlation length exponent ν is found to be t/ν=2.276±0.012. Combining this with the accepted value ν=0.88±0.02 gives t=2.003±0.047, very close to the upper bound t=2 recently proposed by Golden. Studying the connectivity of lattices up to (200${)}^3$, we estimate that the bond percolation threshold ${\mathit{p}}_{\mathit{c}}$=0.2488 3±0.000 05, slightly smaller than some recent estimates, and have also confirmed the accepted value of ν.