Dergiler / ARI The Bulletin of the Istanbul Technical University / 2004 / Cilt: 54 - Sayı: 2

Knot probability for self-avoiding loops on a cubic lattice

Knot probability for self-avoiding loops on a cubic lattice

Yacov KANTOR, Mehran KARDAR

Sayfa
1–5
DOI
—

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 method produces knot probabilities slightly higher than those obtained by Yao et al.[1] using a Monte Carlo method to generate loops.