Triple minima in free energy of semiflexible polymers

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness for finite chains of length L. We find that the polymer properties obtained in this ensemble are "qualitatively" different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.