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arXiv · hep-lat/9302003

New Lower Bounds on the Self-Avoiding-Walk Connective Constant

Takashi Hara·Gordon Slade·Alan D. Sokal
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Abstract

We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high $d$, and in fact agree with the first four terms of the $1/d$ expansion for the connective constant. The bounds are the best to date for dimensions $d \geq 3$, but do not produce good results in two dimensions. For $d=3,4,5,6$, respectively, our lower bound is within 2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.

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Takashi Hara, Gordon Slade, Alan D. Sokal. 1993-02-11. New Lower Bounds on the Self-Avoiding-Walk Connective Constant. https://doi.org/10.1007/bf01048021

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