Nonuniversality In the Collapse of 2-dimensional Branched Polymers

In this paper we study the complete phase diagram of a model of interacting branched polymers. The model we consider is a lattice animal one, where the collapse transition can be driven both by a contact fugacity between two occupied nearest neighbours and by a fugacity related to each occupied edge. Using a Potts model formulation of the problem we conjecture the existence of two different universality classes for the theta transitions (with thermal exponents, nu and phi, equal to (1/2, 2/3) and (8/15, 8/15)), separated by a higher-order percolation point. We also present convincing numerical evidence for these exponent values using a transfer-matrix approach. We discuss the possibility of a collapse-collapse transition and we predict the behaviour of our model when an adsorbing surface is included.