Adsorbing and collapsing directed animals

A model of a self-interacting directed animal, which also interacts with a solid wall, is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition. The directed animal i s confined to a 45 degrees wedge, and it interacts with one of the walls of this wedge. The existence of a thermodynamic limit in this model shown, an d the presence of an adsorption transition is demonstrated by using constru ctive techniques. By comparing this model to a process of directed percolat ion, we show that there is also a collapse or theta -transition in this mod el. We examine directed percolation in a wedge to show that there is a coll apse phase present for arbitrary large values of the adsorption activity. T he generating function of adsorbing directed animals in a half-space is fou nd next from which we find the tricritical exponents associated with the ad sorption transition. A full solution for a collapsing directed animal seems intractible, so instead we examine the collapse transition of a model of c olumn convex directed animals with a contact activity next.