Localization of random copolymers and the Morita approximation

We discuss and analyse the Morita approximation for a number of different models of quenched random copolymer localization at the interface between two immiscible liquids. We focus on two directed models, bilateral Dyck paths and bilateral Motzkin paths, for which this approximation can be carried through analytically. We study the form of the phase diagram and find that the Morita approximation gives phase boundaries which are qualitatively correct. This is also true when a monomer-interface interaction is included in the model. When this interaction is attractive it can lead to separation of the phase boundaries, which is also a feature of the quenched problem. We note the existence of non-analytic points on the phase boundaries which may reflect tricritical points on the phase boundaries of the full quenched average problem. In certain regions of the phase plane this approximation can be extended to the self-avoiding walk model.