Vol. 54 No. 02 (2004): Volume 54 Number 02, June 2004

Knot Probability for Self-Avoiding Loops on a Cubis Lattice

Yacov Kantor
School of Physics and Astronomy, Raymond and Beverly Sackler Fac. of Exact Sciences, Tel Aviv Univercity Tel Aviv 69978, Israel
Mehran Kardar
Department of Physics, Massachusetts Institute of Technology, USA

Published 07/01/2004


  • knots,
  • self-avoiding loops,
  • cubic lattice

How to Cite

Kantor, Yacov, and Mehran Kardar. 2004. “Knot Probability for Self-Avoiding Loops on a Cubis Lattice”. ITU ARI Bulletin of Istanbul Technical University 54 (02):1 - 5. https://ari.itu.edu.tr/index.php/ituari/article/view/46.


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.