Knot Probability for Self-Avoiding Loops on a Cubic Lattice

TL;DR

This paper studies the likelihood of knot formation in self-avoiding loops on a cubic lattice, using an unbiased sampling method to analyze how knot probability varies with loop size, confirming previous Monte Carlo findings.

Contribution

Introduces an unbiased sampling method for self-avoiding loops and analyzes knot probabilities, validating prior Monte Carlo results.

Findings

Knot probability increases with loop size.

Sampling method produces unbiased SALs.

Results corroborate previous Monte Carlo studies.

Abstract

We investigate the probability for appearance of knots in self-avoiding loops (SALs) on a cubic lattice. A set of N-step loops is generated by attempting to combine pairs of (N/2)-step self-avoiding walks constructed by a dimerization method. We demonstrate that our method produces unbiased samples of SALs, and study the knot formation probability as a function of loop size. Our results corroborate the conclusions of Yao et. al. with loops generated by a Monte Carlo method.