Percolation conductivity exponent t to second order in epsilon =6-d.

Abstract

We use the replicated zero-state Potts-model formulation of the randomly diluted resistor network and the dimensional regularization form of the renormalization group to calculate the exponent t governing the growth of the macroscopic conductivity \ensuremath{\Sigma} near percolation threshold to second order in \ensuremath{\epsilon}=6-d. We find t=(d-2)\ensuremath{\nu}+${\ensuremath{\varphi}}_{1}$ where ${\ensuremath{\varphi}}_{1}$=1+\ensuremath{\epsilon}/2\ifmmode\times\else\texttimes\fi{}3\ifmmode\times\else\texttimes\fi{}7+4${\ensuremath{\epsilon}}^{2}$${/3}^{2}$ \ifmmode\times\else\texttimes\fi{}${7}^{3}$.