The collapse transition for the lattice trees

The authors consider a lattice tree model for the collapse of dilute branched polymers in the good solvent regime in which the collapse is driven by a near-neighbour contact fugacity. They describe some rigorous results, including bounds, for the temperature dependence of the reduced limiting free energy and compare these results with numerical estimates derived from exact enumeration data. From the specific heat, they estimate the collapse temperature Tc and the cross-over exponent phi 0 in two and three dimensions. They find phi 0=0.60+or-0.03 (d=2) and phi 0=0.82+or-0.03 (d=3). Finally, they speculate on a possible roughening transition which may occur at a temperature Tr(Tc.