Distribution Function for Self-Avoiding Walks

Publisher Website
Google Scholar
Abstract
In this paper the asymptotic behavior of the distribution function for self-avoiding walks is derived from the generating function Gn(θ), where n is the number of steps and θ is a variable of the function. The asymptotic form of Gn(θ) for large n is determined as follows: First, from the subadditive property of lnGn(θ) we prove rigorously the existence of κ(θ) = limn→∞(1 / n) lnGn(θ) and determine its upper and lower bounds. Second, from the enumeration data for small n we determine the form of Gn(θ) exp[− nκ(θ)] for large n. The relation between δ and ν, defined, respectively, by Fn(x) ∼ exp[− (x / xn)δ] and xn ∼ nν, are derived from the distribution function thus obtained.

This publication has 13 references indexed in Scilit: