Force signature of the unzipping transition for strip confined two-dimensional polymers

We find and analyse the exact solution of two friendly walks, modelling polymers, confined between two parallel walls in a two-dimensional strip (or slit) where the polymers interact with each other via an attractive contact interaction. In the bulk, where the polymers are always far from any walls, there is an unzipping transition between phases where the two walks drift away for low attractive fugacity (high temperatures) and bind together for high attractive fugacities (low temperatures). Previously this has been used to model the denaturation of DNA. In a strip the transition is not sharp. However, we demonstrate that there is an abrupt change in the repulsive force exerted on the walls of the strip that can be calculated exactly. We suggest that this change in the force could be exploited to provide an experimental signature of the unzipping transition. (paper)