Persistence length of semiflexible polymers and bending rigidity renormalization

TL;DR

This paper derives the persistence length of semiflexible polymers and membranes through an exact real-space renormalization group approach, revealing exponential decay of bending rigidity and providing a new perspective on defining persistence length.

Contribution

It introduces a novel exact renormalization group method to calculate the persistence length, differing from traditional perturbative approaches for membranes.

Findings

Renormalized bending rigidity vanishes exponentially at large scales.

Persistence length matches tangent correlation function results for polymers.

Provides a new definition of persistence length for membranes.

Abstract

The persistence length of semiflexible polymers and one-dimensional fluid membranes is obtained from the renormalization of their bending rigidity. The renormalized bending rigidity is calculated using an exact real-space functional renormalization group transformation based on a mapping to the one-dimensional Heisenberg model. The renormalized bending rigidity vanishes exponentially at large length scales and its asymptotic behaviour is used to define the persistence length. For semiflexible polymers, our result agrees with the persistence length obtained using the asymptotic behaviour of tangent correlation functions. Our definition differs from the one commonly used for fluid membranes, which is based on a perturbative renormalization of the bending rigidity.