Phase diagram of force-induced DNA unzipping in exactly solvable models

The mechanical separation of a double helical DNA structure induced by forces pulling apart the two DNA strands (“unzipping”) has been the subject of recent experiments. Analytical results are obtained within various models of interacting pairs of directed walks in the $(1,1,\dots ,1)$ direction on the hypercubic lattice, and the phase diagram in the force-temperature plane is studied for a variety of cases. The scaling behavior is determined at both the unzipping and melting transitions. We confirm the existence of a cold denaturation transition recently observed in numerical simulations: for a finite range of forces, the system is unzipped by decreasing the temperature. The existence of this transition is rigorously established for generic lattice and continuum space models.