English

Improved lower bounds on the connective constants for two-dimensional self-avoiding walks

Statistical Mechanics 2009-11-10 v2

Abstract

We calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, (4.82)(4.8^2), and (3.122)(3.12^2) lattices. The bound is found by Kesten's method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds are obtained from recent exact enumeration data for the number of self-avoiding walks and compared to current best available upper bounds from other methods.

Keywords

Cite

@article{arxiv.cond-mat/0409381,
  title  = {Improved lower bounds on the connective constants for two-dimensional self-avoiding walks},
  author = {Iwan Jensen},
  journal= {arXiv preprint arXiv:cond-mat/0409381},
  year   = {2009}
}
R2 v1 2026-07-22T11:07:56.233Z