Crossover behavior for self-avoiding walks interacting with a surface

Exact enumeration data have been analyzed by the partial-differential-approximation method for the adsorption (special) transition in self-avoiding walks attached to penetrable and impenetrable surfaces. Estimates of the crossover exponent cphi are consistent with 0.28±{}0.05 (D=2) and 0.40±{}0.01 (D=3) for the penetrable surface, and 0.51±{}0.04 (D=2) and 0.54±{}0.07 (D=3) for the impenetrable surface.