Stretching of a polymer below the Theta point

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 lattice. A ground state analysis of finite length chains shows that the globule unfolds via multiple steps, corresponding to transitions between different minima, in both cases. In the infinite length limit, these intermediate minima have a qualitative effect only in $d=2$. The phase diagram in d=2 is determined using transfer matrix techniques. Energy-entropy and renormalization group arguments are given which predict a qualitatively correct phase diagram and a change of the order of the transition from d=2 to d=3.