Numerical study of self-avoiding walks on lattices and in the continuum

We propose a consistent description for the mean-square length of self-avoiding walks on lattices and in the continuum, based on careful numerical studies in two and three dimensions. Existing exact enumerations for various lattices are combined with new precise Monte Carlo results and are analyzed according to the best available theoretical models. Small but persistent differences from two-parameter dimensions for walks on different lattices are discussed. The Domb-Barrett equation for the mean-square end-to-end length of a walk is adjusted to reflect the most accurate estimates of the coefficients and exponents, and a similar equation is proposed for two-dimensional walks. Finally, new results for self-avoiding walks in the continuum are interpreted within the framework of the Domb-Joyce model as being consistent with lattice results.