Renormalized finite cluster expansion.

There are many statistical systems in which degrees of freedom can be grouped according to their degree of correlation. We develop a cluster expansion method for these systems based on selecting finite clusters of the most strongly interacting degrees of freedom. The starting point is Kubo's generalized cumulant formalism. We show how this expansion can be normalized, that is, how the contributions of infinite classes of articulated finite clusters can be resumed. The elimination of articulated clusters from the renormalized expansion generates modified interactions in the finite clusters remaining in the expansion.