Effects of surfaces on resistor percolation

Abstract

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents $ϕ_{\mathcal S \mathnormal}$ and $ϕ_{\mathcal S \mathnormal}^\infty$ for the special and the ordinary transition, respectively, to one-loop order.