Some tests of scaling theory for a self-avoiding walk attached to a surface

Abstract

The authors have defined analogues of the surface and layer susceptibilities of a semi-infinite magnetic system for the self-avoiding walk model of a polymer attached to a surface. Surface scaling relations between exponents appearing in the magnetic problem, as well as a recent renormalisation group exponent relationship, should apply to the self-avoiding walk case and extensive series expansions of the analogues of these susceptibilities have been generated for the square and simple cubic lattices. Analyses of these series show that surface scaling holds for the self-avoiding walk problem in both two and three dimensions but that the renormalisation group argument gives incorrect values of the exponents in two dimensions.