Thermodynamically stable phases for semiflexible polymers characterized by knots of specific topologies

We investigate the influence of bending stiffness on the conformational phases of a semiflexible bead-stick homopolymer and present the pseudo-phase diagram for the complete range of semiflexibility, from flexible to stiff. By varying the bending stiffness, the model exhibits different pseudo phases governed by bent, hairpin or toroidal conformations. In particular, we find thermodynamically stable phases characterized by knots of specific topologies. The transitions into these ``knotted'' phases from other ordered phases are quite unusual in that they display clear phase coexistence but almost no change in the mean total energy and hence no latent heat. It will be explained how we arrive at these intriguing results by computer simulations based on a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method and discussed how one can understand these effects by basic statistical physics reasoning.