Abstract. The authors consider a number of related lattice models of branched polymers in dilute solution in which the polymer is modelled as a tree or as an animal. In order to model the effect of the thermodynamic properties of changing the temperature, or the quality of the solvent, they consider counting cycles in animals and near-neighbour contacts in both animals and trees. They show that the free energies of these models have common features and derive rigorous upper and lower bounds on the temperature dependence of the free energies. Finally, they derive series data for several of these models and compare their estimates of the limiting free energy with the rigorous bounds.

Print publication: Issue 22 (21 November 1990)