  Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001))
considered a model of DNA denaturation in which excluded volume effects within
each strand are neglected, while mutual avoidance is included. Using an
approximate scheme they found a first order denaturation. We show that a first
order transition for this model follows from exact results for the statistics
of two mutually avoiding random walks, whose reunion exponent is c > 2, both in
two and three dimensions. Analytical estimates of c due to the interactions
with other denaturated loops, as well as numerical calculations, indicate that
the transition is even sharper than in models where excluded volume effects are
fully incorporated. The probability distribution of distances between
homologous base pairs decays as a power law at the transition.
