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'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 $1\le D<2$ and $ϵ>0$ sufficiently small, where $ϵ=D-(2-D)\frac{d}{2}$.

Comments: 47 pages in simple Latex, PAR-LPTHE 9346