Continuous and first-order polymer adsorption on hierarchical fractal walls

Polymer adsorption on fractally rough walls of varying dimensionality is st udied by renormalization group methods on hierarchical lattices. Exact resu lts are obtained for deterministic walls. The adsorption transition is foun d continuous for low dimension d(w) of the adsorbing wall and the correspon ding crossover exponent phi monotonically increases with d(w), eventually o vercoming previously conjectured bounds. For d(w) exceeding a threshold val ue d(w)* phi becomes one and the transition changes to first order. d(w)* > d(saw), the fractal dimension of the polymer in the bulk. An accurate nume rical approach to the same problem with random walls gives evidence of the same scenario.