Knot Probability for Self-Avoiding Loops on a Cubic Lattice

2003/05/11 by Yacov Kantor, Mehran Kardar
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.soft

paper · pdf

published as ARI (Bull. Istanbul Tech. Univesity) 54(2), 1 (2004) · RevTeX4, 4 pages, 4 eps figures

arxiv created 2003/05/11 · arxiv updated 2009/11/30

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.

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