Copolymer at a selective interface and two-dimensional wetting: a grand canonical approach

We consider two different problems involving the localization of a single p olymer chain: (i) a periodic AB copolymer at a selective fluid-fluid interf ace, with the upper (resp. lower) fluid attracting A (resp. B) monomers (ii ) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization tra nsition in a grand canonical approach. We recover the results obtained in p revious studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some fi nite size effects are also determined and tested numerically.