On the phase diagram of branched polymer collapse

The phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the $q\to 1$ limit of an extension of the $q-$ states Potts model. Exact solution on the Bethe lattice and Migdal-Kadanoff renormalization group calculations show that there is a line of $\theta$ transitions from the extended to a single compact phase. The $\theta$ line, governed by three different fixed points, consists of two lines of extended--compact transitions which are in different universality classes and meet in a multicritical point. On the other hand, directed branched polymers are shown to be completely determined by the strongly embedded case and there is a single $\theta$ transition which is in the directed percolation universality class.