Adsorption of a self-avoiding walk, a real space renormalisation group study of d=2,3

Abstract

The author presents a real space renormalisation group calculation for the adsorption of a single self-avoiding walk in d dimensions at a (d-1)-dimensional impenetrable wall. The case d=3 is used to check the method. For d=2 the result for the crossover exponent phi gives phi =0.55+or-0.15. This, in connection with enumerations of Ishinabe (1982), clearly rules out de Gennes' (1972, 1976, 1977) conjecture phi =1-v also for the case d=2. For d=2 cells up to 6*6 are used, for d=3 cells up to 3*3*3.