Collapse transition of branched polymers with a tunable number of loops

Branched polymers described by bond lattice animals will undergo a collapse transition if the fugacity for loops is increased. Based on analysis of extensive enumerations by Sykes and collaborators of cubic-lattices embeddings, we conclude that the specific heat diverges if the tricritical point is approached, keeping the number of occupied sites constant, but exhibits a cusp if the number of bonds is fixed. This behavior is explained in terms of a "Fisher renormalization."