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

Abstract

© 2020 Elsevier B.V. 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. In one case the transition occurs at infinite temperature so is less interesting but in other cases occur at finite temperatures. We analyse the phase transition associated in 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.