Effective medium treatments of random simple square and simple cubic conductance networks

A simple treatment of networks containing conductances g_A and g_B gives an exact formula for the conductivity in terms of g_A, g_B, the fraction b of conductances g_B and a quantity lambda . Setting lambda =d^-1 in d dimensions 1 - 2/pi in two dimensions and 0.210 in three dimensions yields effective medium results for the bond, two-dimensional 'non-overlapping' site and three-dimensional 'non-overlapping' site problems respectively. This is shown to be a good approximation for all values of g_B/g_A and b. For the ordinary site problem the lambda values 1 - 2/pi and 0.210 yield good approximations only when b to 0 or g_B=0 and lambda increases by approximately 50% as b to 1 with g_B not=0.