Theory of continuum percolation I. General formalism

Details Theory of continuum percolation I. General formalism Theory of continuum percolation I. General formalism

1996-06-26

arxiv.org/abs/cond-mat/9606195v1

Phys Rev E 54 (1996) 5992

Physics

Condensed Matter

26 pages, Latex

Scientific paper

10.1103/PhysRevE.54.5992

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ 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, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.

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