Abstract
We consider a number of lattice animal models for the collapse transition exhibited by branched polymers in dilute solution. In all models, the collapse is driven by either some kind of near-neighbour fugacity or cycle fugacity. We describe rigorous upper and lower bounds on the temperature dependence of the limiting free energy and compare these bounds with numerical estimates derived using new exact enumeration data. Finally, we comment on the difficulties associated with the interpretation of results for the specific heat.
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