Branched polymers on Bethe and Husimi lattices.

Abstract

We study a branched polymer model defined on a lattice with coordination number q. We introduce q different site fugacities, corresponding to all possible incoming polymer bonds on a site. The model is solved exactly on the treelike Bethe and Husimi lattices. In particular, the interesting case of two nonzero fugacities is treated. The model presents qualitatively different phase diagrams when the coordination number of the lattice is changed. The system has in some cases one polymerized phase, but in other cases a second polymerized phase appears. The conditions for the existence of this second poly- merized phase are established.