Vesicles, the tricritical-0-state Potts-model, and the collapse of branched polymers

Abstract

We relate a cycle model for the collapse of branched polymers without holes (in d = 2) to the problem of self-avoiding rings with an area fugacity, studied in the context of vesicles. This relation together with arguments which show that the collapse transition of branched polymers (with holes) is described by the tricritical-zero-state Potts model allows a determination of all critical exponents at this collapse point; nu = 1/2, phi = 2/3, tau = 2, in agreement with numerical results. We also comment on the universality of this result.