Renormalization Group Approach to Interacting Crumpled Surfaces: The hierarchical recursion

Abstract

We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson&#39;s renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-Gaussian fixed point for $1 \leq D< 2$ and $ε>0$ sufficiently small, where $ε= D - (2-D) {d\over 2}$.