Statistical Physics Group

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 qâ+Ž1 limit of an extension of the q-state Potts model. Exact solution on the Bethe lattice and Migdal-Kadanoff renormalization group calculations shows that there is a line of Ξ transitions from the extended to a single compact phase. The Ξ 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 Ξ transition which is in the directed percolation universality class.