2001/03/31 by Akihisa Yao, Hiroshi Matsuda, Hiroshi Tsukahara +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Materials and Mechanics #Geometric and Algebraic Topology #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/34/37/310
LaTeX2e, 21 pages, 8 figure
arxiv created 2001/08/28 · openalex publication_date 2001/09/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The knotting probability is defined by the probability with which an N -step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of N . In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be 2.5 × 10 5 on the cubic lattice.