Conductivity for the site-percolation problem by an improved effective-medium theory

The effective-medium theory has been presented by many authors and widely applied. In particular, the theory is accepted as a very good first approximation for the conductivities of inhomogeneous continuous media, of random-resistor networks, and of the bond-percolation problem. But the discrepancy between the conductivity given by theory and that of the site-percolation problem is substantial. In this Brief Report we improve the theory for this problem and propose three equations for the effective conductivity in the site-percolation problem. Although the three equations are empirical, the conductivities given by these equations agree well with data from computer simulations and actual experiments for the site-percolation problem except for the (extreme) vicinity of the critical percolation probability.