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

A R Conway·I G Enting·A J Guttmann
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Abstract

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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A R Conway, I G Enting, A J Guttmann. 1992-11-27. Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice. https://doi.org/10.1088/0305-4470%2F26%2F7%2F012

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