2 INTERACTING DIRECTED POLYMERS - EXACT SOLUTION

We consider two interacting, directed polymer chains on the square lattice and solve the problem exactly by transfer matrix methods. Our model can also be considered to describe polymer adsorption to a thermally fluctuating (rough) surface or to model the wetting phenomena for three coexisting phases. We found that for strong enough attraction the two chains stick together, at the transition point the fraction of monomers at contact linearly increases with the interaction potential. Polymer adsorption to a smooth, rigid wall shows the same critical behaviour, thus thermal fluctuations of the substrate are irrelevant.