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

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= 5 2 and ν= 3 5 for the face‐centered cubic lattice and δ=4 and ν= 3 4 for the triangular lattice. Here, δ and ν are defined, respectively, by F n (x)∼ exp [−(|x|/x n ) δ ] and x n ∼n ν , 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.