Exact solutions of directed walk models of polymeric zipping with pulling in two and three dimensions

TL;DR

This paper provides exact solutions for directed polymer zipping models in two and three dimensions, analyzing phase transitions and including effects of pulling forces, with solutions expressed via elliptic integrals.

Contribution

It offers the first exact solutions for directed polymer zipping models in 2D and 3D, incorporating pulling forces and phase transition analysis.

Findings

Exact solutions in terms of elliptic integrals for 3D models.

Characterization of phase transitions and scaling behavior.

Impact of pulling force on zipping transition.

Abstract

We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the solutions are written in terms of complete elliptic integrals. We analyse the phase transition associated with each model giving the scaling of the partition function. We also extend the models to include a pulling force between one end of the pair of paths, which competes with the attractive monomer-monomer interactions between the polymers.