The order of the localization transition for a random copolymer

We use Monte Carlo methods and a scaling analysis to estimate the crossover exponent for a model of the localization transition for a random copolymer at the interface between two immiscible liquids. The model that we use is a directed walk in two dimensions. We find evidence that the nature of the phase transition is different in different regions of the phase diagram. This agrees with previous results for a self-avoiding walk model. We also use exact enumeration and series analysis methods to estimate the locations of the phase boundaries and compare our results to a rigorous bound obtained by partial annealing