Theory of Continuum Percolation Ii. Mean Eld Theory

I use a previously introduced mapping between the continuum per-colation model and the Potts uid to derive a mean eld 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 = 1, = 1 and = 0:5, which are identical with the mean eld exponents of lattice percolation. The critical density in this approximation is c = 1=V y e where V y e = R d~ x p(~ x)fexpp?v(~ x)=kT ] ? 1g. p(~ x) is the binding probability of two particles separated by ~ x and v(~ x) is their interaction potential.