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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.
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Domb et al. (1969) studied this question.
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