Conductivity of continuum percolating systems

We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be mapped onto a bond percolation model where the conductance sigma of randomly occupied bonds is drawn from a probability distribution of the form sigma(-a). Employing the methods of renormalized field theory we show to arbitrary order in epsilon expansion that the critical conductivity exponent of the Swiss-cheese model is given by t(SC)(a) = (d-2)nu + max[phi,(1-a)(-1)], where d is the spatial dimension and nu and phi denote the critical exponents for the percolation correlation length and resistance, respectively. Our result confirms a conjecture that is based on the "nodes, links, and blobs" picture of percolation clusters.