On two-dimensional self-avoiding random walks

Abstract

Following Nienhuis' (1982) exact evaluation of the connective constant of the honeycomb lattice self-avoiding walk model, and the exact exponent values he has conjectured, the author has re-examined the available data on all three regular two-dimensional lattices. In the case of the triangular lattice the author has additionally corrected and extended the extant series. The author finds support for Nienhuis' value gamma =111/32 for all three lattices, and further finds that alpha =1/2 for all three lattices, as given by Nienhuis' result nu =3/4 and the hyperscaling relation d nu =2- alpha . The author is unable to find any consistent evidence of a 'correction-to-scaling' exponent Delta 1<1 f..