title: Mean-field conductivity in a certain class of networks.
abstract: We consider resistor networks, which are lattices with bonds represented by conductors and some of the bonds removed. It is known that effective medium theories predict that the effective conductivity of such networks is a linear function of the number of bonds present above the percolation threshold, but exact results for completely random networks deviate from linearity. We show that if instead we take a randomly chosen tree spanning the lattice and then start adding bonds to it at random, the conductivity changes linearly with the number of added bonds and coincides with the effective medium result for a given bond concentration. We also make comparisons with some related models.
authors.affiliation: Département de Physique, Université de Montréal, Case Postale 6128, Succursale Centre-ville, Montréal, Québec, Canada H3C 3J7. mykyta.chubynsky@umontreal.ca
authors.forename: M V
authors.initials: MV
authors.lastname: Chubynsky
authors.forename: M F
authors.initials: MF
authors.lastname: Thorpe