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

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

1993-02-11

arxiv.org/abs/hep-lat/9302003v1

J.Statist.Phys. 72 (1993) 479-517; Erratum-ibid. 78 (1995) 1187-1188

Physics

High Energy Physics

High Energy Physics - Lattice

35 pages, 388480 bytes Postscript, NYU-TH-93/02/01

Scientific paper

10.1007/BF01048021

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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