Longitudinal size exponent for square-lattice directed animals

Abstract

Series expansions for the longitudinal gyration radius of square-lattice directed-site animals to order N=39 are given. This doubles the length of the available series. Analysis of the series yields the estimate nu /sub ///=0.81722+or-0.00005, which excludes the conjecture nu /sub ///=9/11 based on phenomenological renormalization and shorter series, but is consistent with the later phenomenological renormalization estimate of Dhar: nu /sub ///=0.81733+or-0.00005.