Self-avoiding walks in a slab with attractive walls

Abstract

We consider a self-avoiding walk confined between two parallel planes (or lines), with an energy term associated with each vertex of the walk in the confining planes. We allow the energy terms to be different for the top and bottom planes. We use exact enumeration and Monte Carlo methods to investigate the force between the confining planes and how it depends on the width of the slab and on the interaction energy terms. The phase diagram is qualitatively similar to that found for a directed walk model.