Flory Exponents from a Self-Consistent Renormalization Group

TL;DR

This paper derives the Flory exponent for isotropic polymers using a self-consistent renormalization group approach, confirming the classical Flory result through an epsilon-expansion and background field analysis.

Contribution

It introduces a self-consistent RG method relating the wandering exponent to background field correlations, providing a new derivation of the Flory exponent.

Findings

For dimensions d<4, ν=3/(d+2)

For dimensions d≥4, ν=1/2

The method confirms classical Flory results

Abstract

The wandering exponent $\nu$ for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the wandering exponent to the exponent in the background field through an $\epsilon$-expansion. We then choose the background field to have the same correlations as the individual polymer, thus self-consistently solving for $\nu$. We find $\nu=3/(d+2)$ for $d<4$ and $\nu=1/2$ for $d\ge 4$, which is exactly the Flory result.