A detailed field theory for RNA-like molecules with periodic base sequence

Abstract

This work examines a field theory for RNA-like molecules in a good solvent. The field theory is based on a lattice model for single- and double-strand RNA with a periodic base sequence, and otherwise contains all known relevant details (polymer types, polymer lengths and interactions). As for the somewhat less explicit $O\left(n\right)$-symmetric model there is a close relation to the conventional one-component branched polymer and the associated Lee-Yang problem. We further elucidate this relation. We derive exact results in the limiting cases of nearly complete denaturation and nearly complete renaturation. The single-strand critical exponent $\nu_{\varphi}$ is calculated in two-loop order.