Classification of Perturbations for Membranes with Bending Rigidity

TL;DR

This paper provides a comprehensive classification of the renormalization-group flow for impurity-like marginal operators in membranes with bending rigidity, focusing on their scaling behavior near the critical dimension.

Contribution

It introduces a complete classification scheme for these operators using characteristic functions on R^2 x R^2, advancing understanding of membrane elasticity at criticality.

Findings

Classification of impurity-like marginal operators

Characterization using functions on R^2 x R^2

Insights into membrane behavior near critical dimension

Abstract

A complete classification of the renormalization-group flow is given for impurity-like marginal operators of membranes whose elastic stress scales like (\Delta r)^2 around the external critical dimension d_c=2. These operators are classified by characteristic functions on R^2 x R^2.