CLUSTER STRUCTURE OF COLLAPSING POLYMERS

In order to better understand the geometry of the polymer collapse tra nsition, we study the distribution of geometric clusters made up of th e nearest neighbor interactions of an interacting self-avoiding walk. We argue for this new correlated percolation problem that in two dimen sions, and possibly also in three dimensions, a percolation transition takes place at a temperature lower than the collapse transition. Henc e this novel transition should be governed by exponents unrelated to t he theta-point exponents. This also implies that there is a temperatur e range in which the polymer has collapsed, but has no long-range clus ter structure. We use Monte Carlo to study the distribution of cluster s on the simple cubic and Manhattan lattices. On the Manhattan lattice , where the data are most convincing, we find that the percolation tra nsition occurs at omega(p) = 1.461(3), while the collapse transition i s known to occur exactly at omega(0) = 1.414.... We propose a finite-s ize scaling form for the cluster distribution and estimate several of the critical exponents. Regardless of the Value of omega(p), this perc olation problem sheds new light on polymer collapse.