Critical exponents for surface interacting self-avoiding lattice walks. II. The square lattice

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Abstract
Critical exponents for the two-dimensional version of adsorption of a polymer chain at an interface are estimated as δa≃1.9 and ζ≃1.5 from the exact enumeration of self-avoiding walks up to 21 terms on the square lattice, where δa and ζ are defined from the respective dependences of the free energy and the thickness of adsorption layer on monomer–surface interaction; ζ is to be estimated to be about unity for three-dimensional lattices. These values are different from the scaling predictions of de Gennes: δa=4 and ζ=3 in two dimensions, and ζ=1.5 in three dimensions. An assumption in the scaling treatment is examined by using the exact enumeration data in order to explain the discrepancy.