Force-induced unfolding of a homopolymer on a fractal lattice: exact results versus mean-field predictions

We study the force-induced unfolding of a homopolymer on the three-dimensional Sierpinski gasket. The polymer is subject to a contact energy between nearest-neighbour sites not consecutive along the chain and to a stretching force. The hierarchical nature of the lattice we consider allows for an exact treatment which yields the phase diagram and the critical behaviour. We show that for this model mean-field predictions are not correct; in particular, in the exact phase diagram there is no low-temperature re-entrance, and we find that the force-induced unfolding transition below the theta temperature is of second order.