Adsorption and collapse of self-avoiding walks in three dimensions: A Monte Carlo study

We consider self-avoiding walks on the simple cubic lattice, with a unit degree vertex at the origin and confined to the half-space . In addition the walks interact with the plane z = 0 and have a vertex-vertex interaction within the walk, so that the walk can adsorb at the surface z = 0 and also undergo collapse. We investigate the interaction between collapse and adsorption using Monte Carlo methods, and explore the form of the phase diagram.