A low temperature expansion for classical N-vector models III. A complete inductive description, fluctuation integrals

We give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical N-vector models described in the paper [1], and we formulate the main theorems of this sequence of papers. This description includes now all the "large field" domains, which we've excluded from the discussions of [1, 4]. We apply the renormalization transformation to a density satisfying the inductive hypotheses, we introduce "large field-small field" partitions, and we determine and analyze the fluctuation integrals in the general setting.