The Green$apos$s function approach to adsorption of a random heteropolymer onto surfaces

We study the localization of a heteropolymer with Gaussian distributed random sequences onto an homogeneous surface, the problem which is equivalent to the wetting of an interface at a disordered substrate in two dimensions, via replica trick by using the Green's function technique. We present analytical results of the study of one- and two-replica binding states for two particular cases: (i) nearly statistically symmetric copolymer in the vicinity of the threshold of the annealed problem, and (ii) the asymmetric polymer with the interaction part of the annealed Hamiltonian being nearly zero. In both cases, the localization is due to two-replica binding states. In case (i) the two-replica binding state exists both above and below the localization transition of the annealed problem. In case (ii) the energy of the two-replica binding state at the transition is finite. The exact treatment of the one- and two-replica bound states is used to compute the free energy of the random heteropolymer. A schematic phase diagram of the localization–delocalization transition of the random heteropolymer is suggested.