A universality class for RNA-like polymers and double polymers

TL;DR

This paper develops a field theory for RNA-like polymers, revealing a universal behavior at a critical point where double polymers decouple and form branched structures, with implications for understanding polymer conformations.

Contribution

It introduces a novel field theoretical framework for RNA-like polymers, identifying a universality class and critical behavior involving double and single strands.

Findings

Existence of a stable renormalization group fixed point.

Double polymers become branched polymers at the fixed point.

Critical exponents and equations of state are derived for the model.

Abstract

We examine the statistics of conformations of a linear polymer in a solvent. The polymer is allowed to form double polymers. We closely follow a classical technique to derive a field theory for the problem from an $O\left(n\right)$ symmetric spin model. The field theory is a model for RNA or DNA with constant binding energy per monomer. It is shown that there is a stable renormalization group fixed point, at which the double polymer decouples from the single-strand polymer and becomes a branched polymer of the conventional type with a three-point interaction. To reach this fixed point, at least one parameter must be adjusted. The critical dimension is eight. Fisher-renormalization, equation of state and critical exponents are reproduced in this limit. The single-strand polymer depends on the double-strand polymer and disappears at the critical point, but has its own critical exponents.