  We study pairs of interacting self-avoiding walks on the 3d simple cubic
lattice. They have a common origin and are allowed to overlap only at the same
monomer position along the chain. The latter overlaps are indeed favored by an
energetic gain.
  This is inspired by a model introduced long ago by Poland and Sheraga [J.
Chem. Phys. {\bf 45}, 1464 (1966)] for the denaturation transition in DNA
where, however, self avoidance was not fully taken into account. For both
models, there exists a temperature T_m above which the entropic advantage to
open up overcomes the energy gained by forming tightly bound two-stranded
structures.
  Numerical simulations of our model indicate that the transition is of first
order (the energy density is discontinuous), but the analog of the surface
tension vanishes and the scaling laws near the transition point are exactly
those of a second order transition with crossover exponent \phi=1. Numerical
and exact analytic results show that the transition is second order in modified
models where the self-avoidance is partially or completely neglected.
