A self-avoiding walk model of random copolymer adsorption

We consider a model of random copolymer adsorption in which a self-avoiding walk interacts with a hypersurface defining a half-space to which the walk is confined. Each vertex of the walk is randomly labelled with areal variable which determines the strength of the interaction of that vertex with the hypersurface. We show that the thermodynamic limit of the quenched average free energy exists and is equal to the thermodynamic limit of the free energy for almost all fixed labellings, so the system is self-averaging. In addition we show that the system exibits a phase transition and we discuss the connection between the annealed and quenched versions of the problem