  The mechanical separation of the 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,...,1) direction on the
hypercubic lattice, and the phase diagram in the force-temperature plane is
studied for a variety of cases. The scaling behaviour is determined at both the
unzipping and the melting transition. We confirm the existence of a cold
denaturation transition recently observed in numerical simulations: for a
finite range of forces the system gets unzipped by {\it decreasing} the
temperature. The existence of this transition is rigorously established for
generic lattice and continuum space models.
