A phase cell cluster expansion for a hierarchical Ø 3 4 model

Abstract

The formalism developed in a previous paper is applied to yield a phase cell cluster expansion for a hierarchical ø 3 4 model. The field is expanded into modes with specific renormalization group scaling properties. The present cluster expansion for a vacuum expectation value is formally the natural factorization of each term in the perturbation expansion into the contribution of modes connected to the variables in the expectation via interactions, and that of the complementary set. The expectation value is thus realized as a sum of contributions due to finite subsets of the modes. We emphasize the following additional features: 1) Partitions of unity are not used.