Distribution Function for Self-Avoiding Walks. II. Numerical Part

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Abstract
By using the exact enumeration data of self-avoiding walks on the triangular and face-centered cubic lattices, we determine the asymptotic behavior of the generating function Gn(θ). With this Gn(θ) we find that δ=52 and ν=35 for the face-centered cubic lattice and δ=4 and ν=34 for the triangular lattice. Here, δ and ν are defined, respectively, by Fn(x)∼exp[−(|x|/xn)δ] and xn∼nν, where Fn(x) is a one-dimensional distribution function of the end point lying distance x away from the origin in n steps, and xn behaves as the mean square end-to-end distance.

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