Mean square endpoint separation of off-lattice self-avoiding walks

Abstract

Ten thousand off‐lattice self‐avoiding walks of 500 steps were generated using a new algorithm combining the features of the enrichment procedure of Wall and Erpenbeck and the dimerization procedure of Alexandrowicz. The mean square endpoint separation was tabulated as a function of the number of steps in the walk and fitted to the equation 〈 R N 2 〉=A N γ , where N is the number of steps in the walk. A value for γ of 1.204± 0.014 was obtained, in excellent agreement with values for on‐lattice walks. Earlier investigators using off‐lattice self‐avoiding walks probably obtained higher values of γ because they were limited to 100‐step walks.