Simple model for the DNA denaturation transition

We study pairs of interacting self-avoiding walks {omega(1),omega(2)} on th e 3d simple cubic lattice. They have a common origin omega(0)(1)=omega(0)(2 ), and are allowed to overlap only at the same monomer position along the c hain: omega(i)(1)not equal omega(j)(2) for i not equal j, while omega(i)(1) =omega(i)(2) is allowed. The latter overlaps are indeed favored by an energ etic gain epsilon. This is inspired by a model introduced long ago by Polan d and Sheraga [J. Chem. Phys. 45, 1464 (1966)] for the denaturation transit ion 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 a dvantage to open up overcomes the energy gained by forming tightly bound tw o-stranded structures. Numerical simulations of our model indicate that the transition is of first order (the energy density is discontinuous), but th e analog of the surface tension vanishes and the scaling laws near the tran sition point are exactly those of a second-order transition with crossover exponent phi=1. Numerical and exact analytic results show that the transiti on is second order in modified models where the self-avoidance is partially or completely neglected.