Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice

Details Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice

1992-11-27

arxiv.org/abs/hep-lat/9211062v1

J.Phys.A26:1519-1534,1993

Physics

High Energy Physics

High Energy Physics - Lattice

25 pages + 3 postscript figures. Tex. Uses preprint.sty

Scientific paper

10.1088/0305-4470/26/7/012

We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of $N$ steps is of order $3^{N/4}$ times a polynomial in $N$, and so the approach is greatly superior to direct counting techniques. We have enumerated walks of up to 39 steps. As a consequence, we are able to accurately estimate the critical point, critical exponent, and critical amplitude.

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