English

A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

Mathematical Physics 2015-06-03 v1 Statistical Mechanics Combinatorics math.MP

Abstract

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.

Cite

@article{arxiv.1111.5877,
  title  = {A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice},
  author = {Nathan Clisby and Iwan Jensen},
  journal= {arXiv preprint arXiv:1111.5877},
  year   = {2015}
}

Comments

17 pages, 8 figures, IoP style files

R2 v1 2026-06-21T19:41:18.866Z