Pair connectedness and cluster size

A theory of pair connectedness is developed for fluid as well as lattice systems when the presence of physical clusters of particles in the system is explicitly taken into account. Activity and density expansions, an Ornstein-Zernicke relation and the Percus-Yevick approximation are established in analogy with the theory of the pair-correlation function. A simple application to the percolation problem is given; for a lattice the results are compared with the known solution of the Bethe lattice. For a fluid system the theory is used to investigate the relation of percolation and condensation in a Van der Waals gas, the result shows that an infinite cluster of particles is formed in the gaseous phase, along the coexistence curve, before the critical point is reached.