Self-avoiding walks and polygons on the triangular lattice

Details Self-avoiding walks and polygons on the triangular lattice Self-avoiding walks and polygons on the triangular lattice

2004-09-02

arxiv.org/abs/cond-mat/0409039v2

J. Stat. Mech., P10008 (2004)

Physics

Condensed Matter

Statistical Mechanics

24 pages, 6 figures

Scientific paper

10.1088/1742-5468/2004/10/P10008

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, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.

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