Knot Probability for Self-Avoiding Loops on a Cubic Lattice

Authors :: Kantor, Yacov
Kardar, Mehran
Publication Year :: 2003
Publisher :: arXiv, 2003.
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.<br />Comment: RevTeX4, 4 pages, 4 eps figures