Lattice animal contact models of a collapsing branched polymer

Abstract

The authors consider two lattice animal models for the collapse of dilute branched polymers in a good solvent. In both cases, the collapse is driven by a near-neighbour contact fugacity, the two models differing in the way molecular weights are assessed, either by the site content or the bond content of the animal. They describe some rigorous results, including bounds for the temperature dependence of their reduced limiting free energies on a d-dimensional hypercubic lattice and compare these results with numerical estimates derived from exact enumeration data. From the specific heat, they estimate the collapse temperature of both models on a variety of lattices. In addition, they estimate the cross-over exponent phi and find that for both models phi =0.60+or-0.03 (d=2) and phi =0.82+or-0.02 (d=3).