A Mass Zero Cluster Expansion

Convergence is proven for the mass zero cluster expansion presented in Part 1 of this paper. An indication is given of changes necessary to treat the more difficult 2(V~b) 4 model and the lattice dipole gas. 9. Counting I In these sections we will be concerned with enumerating the terms in the cluster expansion in a way suitable for estimation. The complexities are largely notational, and due to the need to consider a number of different cases, there are no real difficulties. Then too, this is a new type of cluster expansion, and its "standard tricks" have to be invented. We will try to give motivation for a number of the avenues taken. 9.A. Representation 1 We here present the representation (labelling) of a single term in the cluster expansion, basically as developed in Sect. 8. In later subsections we will find alternate representations more useful for computation. A term in the cluster expansion is determined by giving 1) A finite sequence