Theory of continuum percolation. II. Mean field theory.

I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic. The critical exponents obtained are β = 1, γ = 1 and ν = 0.5, which are identical with the mean field exponents of lattice percolation. The critical density in this approximation is ρc = 1/V † e where V † e = ∫