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Self-avoiding walks and polygons on the triangular lattice

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

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BibTeXRIS

Iwan Jensen. 2004-10-07. Self-avoiding walks and polygons on the triangular lattice. https://doi.org/10.1088/1742-5468%2F2004%2F10%2Fp10008

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