Two-dimensional anisotropic spiral self-avoiding walks
AJ Guttmann, KJ Wallace
Journal of Physics A: Mathematical and General | Published : 1986
Two models of anisotropic spiral self-avoiding random walks recently proposed by Manna (1984) have been investigated by the method of exact series expansions. The number of such n-step walks, cn, appears to behave like cn approximately constant* mu nnbeta exp( alpha square root n) where both mu , which is known exactly, and the constant factor are model dependent but alpha approximately=0.14 and beta approximately=0.9 appear to be model independent. The mean square end-to-end distance exponent nu =0.855+or-0.02 for both models.