Continuous melting of compact polymers

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by Flory in 1956 Proc. R. Soc. London A 234, 60 (1956)]]. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition and compute exact values of critical exponents at the transition point.