Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm

TL;DR

This paper presents a fast implementation of the pivot algorithm enabling the generation of large samples of 3D self-avoiding walks, leading to a highly accurate estimate of the critical exponent or these walks.

Contribution

The paper introduces a novel, efficient implementation of the pivot algorithm that allows for large-scale sampling and precise estimation of the critical exponent or self-avoiding walks.

Findings

Estimated or 3D self-avoiding walks as 0.587597(7)

Generated walks with up to 33 million steps

Method adaptable to other polymer models

Abstract

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for three-dimensional self-avoiding walks is determined to great accuracy; the final estimate is $\nu=0.587597(7)$. The method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum.