Self-avoiding walks with span limitations. I. The mean square end-to-end distance

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Abstract
Self‐avoiding walks on the simple cubic lattice of lengths up to 11 steps were exactly enumerated. The mean square end‐to‐end distance and its mean square components were recorded as a function of the span separation along one principle Cartesian axis. The molecular weight dependence for narrow spans (thin slabs—up to two lattice spacings) obeys that of a two‐dimensional walk as conjectured by Wall et al. As the slab thickness increases, one encounters a dimensionality transition in the behavior of the mean separations which is compared with similar transitions observed for the self‐avoiding walk in the presence of one interacting barrier. For thick slabs the behavior is three dimensional.

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