Branched polymer approach to the structure of lattice animals and percolation clusters

Abstract

The authors treat the percolation problem as a solution of randomly branched chains, and argue that such chains are swollen by a three-body repulsion acting only within a connected cluster. This type of repulsion should not be subject to the screening effects which inhibit ordinary repulsions. The repulsion becomes relevant below six dimensions. They estimate its effect on the size of a cluster in analogy with Flory's argument for the swelling of linear chains. Above six dimensions the cluster size scales as mass to the 1/4 power, as with isolated branched chains in high dimensions.