Search for a percolation transition in a lattice polymer model

We report the results of Monte Carlo simulation studies of a lattice model, derived from the n=0 vector model, of noncrossing polymers in two and three dimensions. We have searched for evidence of a phase transition characterized by single-chain percolation in the model’s dense phase—the phase in which multiple chains occupy a large fraction of the lattice. Extrapolation methods were used on a series of samples of increasing size in order to probe the large system limit. Our results suggest that in the thermodynamic limit the transition takes place only when the statistical weight for chain ends vanishes.