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

We consider a lattice model of random heteropolymers at the interface betwe en two immiscible solvents. One solvent is preferred by one comonomer, whil e the other solvent is preferred by the other comonomer. We investigate the phase diagram of the system and, in particular, the transition from locali zation at the interface to delocalization into one of the two phases. We pr ove some rigorous results concerning the system and, in particular, show th at 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 ana lysis techniques to map out the form of the phase diagram.