- 93-30 Takashi Hara , Gordon Slade , Alan D.Sokal
- New Lower Bounds on the Self-Avoiding-Walk Connective Constant
Feb 11, 93
(auto. generated ps),
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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