Calculation of the connective constant for self-avoiding walks via the pivot algorithm

TL;DR

This paper introduces a novel application of the pivot algorithm to accurately estimate the connective constant for self-avoiding walks on a cubic lattice, achieving unprecedented precision and scalability.

Contribution

The paper presents a new method using the pivot algorithm to compute the connective constant with high accuracy and efficiency for very long self-avoiding walks.

Findings

Estimated connective constant pprox; 4.684039931(27)

Accurate estimates for the number of long self-avoiding walks

Method scalable to walks with millions of steps

Abstract

We calculate the connective constant for self-avoiding walks on the simple cubic lattice to unprecedented accuracy, using a novel application of the pivot algorithm. We estimate that \mu = 4.684 039 931(27). Our method also provides accurate estimates of the number of self-avoiding walks, even for walks with millions of steps.