Correlations in a Self-Avoiding Walk

Abstract

A fundamental feature of a self‐avoiding walk on a crystal lattice is the correlation between any pair of steps. In this paper, exact enumerations for a number of two‐ and three‐dimensional lattices are used to estimate the moments of this correlation. It is suggested that for a walk of n steps in the limit of large n the correlation can be characterized by a single function which is independent of lattice structure in a given dimension. An algebraic expression is put forward to represent this function. Agreement with Monte Carlo estimates is satisfactory.