Abstract
We provide an upper and a lower bound for the cross-over exponent Φ in polymer adsorption on an impenetrable attractive surface. These bounds are shown to be verified for exactly solvable models where the polymer resides on a fractal lattice. In one of these models we also find a multicritical point where a bulk collapse transition and a surface adsorption transition coexist. A simple real-space renormalization scheme is presented for the square lattice, it gives Φ = 0.48, in close agreement with the presumably exact value 1/2, which coincides with our upper bound.
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