### Abstract

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, = 4.150 797 226(26), and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.

Original language | English |
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Article number | P10008 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2004 |

Externally published | Yes |

### Keywords

- critical exponents and amplitudes (theory)
- series expansions