Stretching of a Polymer below theθPoint

The unfolding of a polymer below the $\theta$ point when pulled by an external force is studied both in $d=2$ on the lattice and in $d=3$ off the lattice. At $T=0$ and for finite length chains, it is found that the globule unfolds via multiple steps, corresponding to transitions between different minima, in both cases. In $d=3$ one of these intermediates is a regular helix. In the infinite length limit, these steps have a qualitative effect only in $d=2$. The phase diagram in $d=2$ is determined via the transfer matrix. To rationalize these results, energy-entropy and renormalization group arguments are given.