  Using a combination of the replica-exchange Monte Carlo algorithm and the
multicanonical method, we investigate the influence of bending stiffness on the
conformational phases of a bead-stick homopolymer model and present the
pseudo-phase diagram for the complete range of semi-flexible polymers, from
flexible to stiff. Although a simple model, we observe a rich variety of
conformational phases, reminiscent of conformations observed for synthetic
polymers or biopolymers. Changing the internal bending stiffness, the model
exhibits different pseudo phases like bent, hairpin or toroidal. In particular,
we find thermodynamically stable knots and transitions into these knotted
phases with a clear phase coexistence, but almost no change in the mean total
energy.
