RENORMALIZATION THEORY FOR HIERARCHICAL-MODELS

A nonperturbative renormalization theory of Euclidean field theories i n hierarchical approximation is presented in this paper. The ultraviol et limit is related to the thermodynamic limit of a polymer system on a multigrid. General methods to present a hierarchical model as a mult igrid polymer system are discussed. We provide a sufficient condition for the existence of the continuum limit by a bound for Moebius transf orms. The use of renormalization conditions for polymer activities is described. We study a recursive calculation scheme for polymer activit ies. We state a general cluster expansion formula, which is useful for estimating Moebius transforms.