Localization transition for a randomly coloured self-avoiding walk at an interface

We consider a lattice model of random heteropolymers at the interface between two immiscible solvents. One solvent is preferred by one comonomer, while the other solvent is preferred by the other comonomer. We investigate the phase diagram of the system and, in particular, the transition from localization at the interface to delocalization into one of the two phases. We prove some rigorous results concerning the system and, in particular, show that there is a phase change as the solvent qualities for the two comonomers are varied. We use Monte Carlo methods and exact enumeration and series analysis techniques to map out the form of the phase diagram.