Localization transition of a random polymer at an interface

An analysis is presented of the phase transitions arising from the presence of a random heteropolymer (RHP) at a flat interface between two fluids whose physicochemical interactions with the different monomers comprising the chain differ from one another. We reexamine the analysis of Garel et al. (Europhys. Lett., 8 (1989) 9) to probe the low temperature adsorbed regime. Utilizing the Martin-Siggia-Rose formulation with Hartree approximation we derive the dynamical equations governing the correlation functions. The long-time limit of the dynamical equations indicate a possible ergodicity-breaking transition of the polymer, corresponding to the localization transition predicted in the above-quoted analysis. However, in contradiction to the analysis of Garel et al., we predict that this phenomenon occurs at a finite temperature. This result contrasts with the behavior that might be expected from studies of 1+1 Directed Polymer in Random Media (DPRM), and resembles the behavior of d +1 DPRM for d > 2. Our conclusions are corroborated by transfer matrix simulations.