Theory of continuum percolation .1. General formalism

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analog with lattice systems. Nevertheless, there is yet no comprehensive theory of this field, A basis for such a theory is provided hen with the introduction of the Potts fluid, a system of interacting s-state spins which are free to move in the continuum. In the s-->1 limit, the Potts magnetization, susceptibility, and correlation functions are directly related to the percolation probability, the mean cluster size, and the pair connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid standard methods of statistical mechanics can therefore be used in the continuum percolation problem.