Critical adsorption of polymers in a medium with long-range correlated quenched disorder

The process of adsorption on a planar wall of long flexible polymer chains in a medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power law x(-a) for large distances x , where x= (r,z) . A field theoretical approach in d=4-epsilon and directly in d=3 dimensions up to one-loop order for the semi-infinite |phi|(4) m-vector model (in the limit m-->0 ) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold T= T(a) , which separates the nonadsorbed region from the adsorbed one, is obtained. Moreover, we calculate the crossover critical exponent Phi and the set of exponents associated with it. We perform calculations in a double epsilon=4-d and delta=4-a expansion and also for a fixed dimension d=3 , up to one-loop order for different values of the correlation parameter 2< a < or =3 . The obtained results indicate that for systems with long-range correlated quenched disorder a different set of surface critical exponents arises. All the surface critical exponents depend on a . Hence, the presence of long-range correlated disorder influences the process of adsorption of long flexible polymer chains on a wall in a significant way.