Abstract
The competition between chain entropy and bending rigidity in compact polymerscan be addressed within a lattice model introduced by P.J. Flory in 1956. Itexhibits a transition between an entropy dominated disordered phase and anenergetically favored crystalline phase. The nature of this order-disordertransition has been debated ever since the introduction of the model. Here wepresent exact results for the Flory model in two dimensions relevant forpolymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict acontinuous melting transition, and compute exact values of critical exponentsat the transition point.