Renormalization Theory for the Self-Avoiding Polymerized Membranes

TL;DR

This paper establishes the renormalizability of a model for self-avoiding polymerized membranes using advanced field theory techniques, enabling the derivation of scaling laws and analysis of various interaction regimes.

Contribution

It extends renormalization methods to non-local interactions in membrane models, providing a framework for perturbative calculations and scaling law derivation.

Findings

Proves renormalizability of the generalized Edwards model for membranes.

Derives hyperscaling relations for configuration and contact exponents.

Analyzes membranes with long-range interactions and at the Theta-point.

Abstract

We prove the renormalizability of the generalized Edwards model for self-avoiding polymerized membranes. This is done by use of a short distance multilocal operator product expansion, which extends the methods of local field theories to a large class of models with non-local singular interactions. This ensures the existence of scaling laws for crumpled self-avoiding membranes, and validates the direct renormalization method used for polymers and membranes. This also provides a framework for explicit perturbative calculations. We discuss hyperscaling relations for the configuration exponent and contact exponents. We finally consider membranes with long range interactions and at the Theta-point.