Critical behavior of transport in lattice and continuum percolation models

It has been observed that the critical exponents of transport in the continuum, such as in the Swiss cheese and random checkerboard models, can exhibit nonuniversal behavior, with values different than the lattice case. Nevertheless, it is shown here that the transport exponents for both lattice and continuum percolation models satisfy the standard scaling relations for phase transitions in statistical mechanics. The results are established through a direct, analytic correspondence between transport coefficients for two component random media and the magnetization of the Ising model, which is based on the observation we made previously that both problems share the Lee-Yang property.