Secondary structures in long compact polymers.

Compact polymers are self-avoiding random walks that visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte Carlo algorithm that uniformly samples compact polymer configurations in an efficient manner, allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self-averaging in the long-chain limit and strictly less than 1. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.