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New lower bounds on the self-avoiding-walk connective constant (1993)

Hara, Takashi ; Slade, Gordon ; Sokal, Alan D.

Springer

Journal of statistical physics 72 (1993), S. 479-517

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ISSN: 1572-9613

Keywords: Self-avoiding walk ; connective constant ; loop erasure ; random walk ; 1/d expansion

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: 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 highd, 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 dimensionsd⩾ 3, but do not produce good results in two dimensions. Ford=3, 4, 5, and 6, respectively, our lower bound is within 2.4%, 0.43%, 0.12%, and 0.044% of the value estimated by series extrapolation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01048021

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