Renormalization Group Approach to Interacting Crumpled Surfaces: The hierarchical recursion

TL;DR

This paper applies Wilson's renormalization group to a hierarchical model of crumpled surfaces, proving the existence of a non-Gaussian fixed point in the scaling limit for certain dimensions and small parameters.

Contribution

It rigorously establishes the scaling limit and fixed point behavior of a hierarchical model of interacting crumpled surfaces using renormalization group techniques.

Findings

Existence of a non-Gaussian fixed point for 1 ≤ D < 2 and small ε.

Rigorous proof of the scaling limit and convergence.

Application of Wilson's renormalization group to a hierarchical surface model.

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 $1 \leq D< 2$ and $\epsilon >0$ sufficiently small, where $\epsilon = D - (2-D) {d\over 2}$.