ADSORPTION AND COLLAPSE OF SELF-AVOIDING WALKS AND POLYGONS IN 3 DIMENSIONS

We consider self-avoiding walks and polygons on the simple cubic latti ce, confined to the half-space z greater than or equal to 0 and intera cting with the plane z = 0. In addition there is a shea-range vertex-v ertex interaction in the walk or polygon which can lead to a collapse transition. We explore the interaction between collapse and adsorption in these systems, and discuss the form of the phase diagram. Key resu lts include a proof of the existence of an adsorption transition for p olygons for every value of the vertex-vertex interaction, a correspond ing proof for walks when the vertex-vertex interaction term is repulsi ve, and a proof that if polygons exhibit a collapse transition, then t he phase boundary between the expanded and desorbed phase and the coll apsed and desorbed phase must be a straight line.