Self-avoiding walks on a simple cubic lattice

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Abstract
Dynamic Monte Carlo simulations, using the pivot algorithm, have been performed on a three‐dimensional simple cubic lattice in order to study statistical properties of self‐avoiding walks of lengths up to about 7200 steps. The scaling properties of the end‐to‐end distribution function and its second moment have been investigated and compared with previous works. The distribution function is found to be in agreement with the enhanced Gaussian scaling form of des Cloizeaux. Some properties of the pivot algorithm, such as the acceptance fraction and the integrated autocorrelation times in three dimensions, are also discussed.