Adsorption and collapse transitions of a linear polymer chain interacting with a surface adsorbed polymer chain

We study the problem of adsorption and collapse transition of a linear polymer chain situated in a fractal container represented by a four-simplex lattice and interacting with a surface-adsorbed linear polymer chain. The adsorbed chain monomers act as pinning sites for the polymer chain. This problem has been solved exactly using real space renormalization group transformation. The resulting phase diagram and critical exponents are given.