Percolative conduction in three dimensions

Abstract

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 \ensuremath{\nu} is found to be t/\ensuremath{\nu}=2.276\ifmmode\pm\else\textpm\fi{}0.012. Combining this with the accepted value \ensuremath{\nu}=0.88\ifmmode\pm\else\textpm\fi{}0.02 gives t=2.003\ifmmode\pm\else\textpm\fi{}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\ifmmode\pm\else\textpm\fi{}0.000 05, slightly smaller than some recent estimates, and have also confirmed the accepted value of \ensuremath{\nu}.