A universality class for RNA-like polymers and double polymers

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.

Four figures

References in corpus (6)

• The massless two-loop two-point function
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Statistical Physics of RNA-folding
• Conformational statistics of randomly-branching double-folded ring polymers
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• Scaling properties of RNA as a randomly branching polymer

Cited by in corpus (1)

• Pseudo-RNA with parallel aligned single-strands and periodic base sequence as a new universality class