Localization of a random copolymer at an interface: an exact enumeration study

We consider a self-avoiding walk on the simple cubic lattice, as a model of localization of a random copolymer at an interface between two immiscible liquids. The vertices of the walk are coloured A or B randomly and independently. The two liquid phases are represented by the two half-spaces z > 0 and z < 0, and the plane z = 0 corresponds to the interface between the two liquids. The energy depends on the numbers of A-vertices with positive z-coordinate and B-vertices with negative z-coordinate. In addition there is a vertex-interface interaction, irrespective of the colour of the vertex. We use exact enumeration and series analysis techniques to investigate the form of the phase diagram and how it changes as the magnitude of the vertex-interface interaction changes