Connective constant of the self-avoiding walk on the triangular lattice

A. J. Guttmann; T. R. Osborn; A. D. Sokal

doi:10.1088/0305-4470/19/13/024

Connective constant of the self-avoiding walk on the triangular lattice

A. J. Guttmann, T. R. Osborn, A. D. Sokal

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Abstract

The author uses a recently developed Monte Carlo method to study the connective constant of the self-avoiding walk (SAW) on the triangular lattice. Assuming gamma =43/32 one finds mu _T=4.15096+or-0.00010+or-0.00026 (95% confidence limits) and mu _T=4.15096+or-0.00020+or-0.00037 (99% confidence limits), where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error. This rules out the conjecture mu _T+ mu _H=6 at the greater than 99% confidence level.

Original language	English (US)
Article number	024
Pages (from-to)	2591-2598
Number of pages	8
Journal	Journal of Physics A: Mathematical and General
Volume	19
Issue number	13
DOIs	https://doi.org/10.1088/0305-4470/19/13/024
State	Published - 1986

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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title = "Connective constant of the self-avoiding walk on the triangular lattice",

abstract = "The author uses a recently developed Monte Carlo method to study the connective constant of the self-avoiding walk (SAW) on the triangular lattice. Assuming gamma =43/32 one finds mu T=4.15096+or-0.00010+or-0.00026 (95% confidence limits) and mu T=4.15096+or-0.00020+or-0.00037 (99% confidence limits), where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error. This rules out the conjecture mu T+ mu H=6 at the greater than 99% confidence level.",

author = "Guttmann, {A. J.} and Osborn, {T. R.} and Sokal, {A. D.}",

year = "1986",

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AU - Guttmann, A. J.

AU - Osborn, T. R.

AU - Sokal, A. D.

PY - 1986

Y1 - 1986

N2 - The author uses a recently developed Monte Carlo method to study the connective constant of the self-avoiding walk (SAW) on the triangular lattice. Assuming gamma =43/32 one finds mu T=4.15096+or-0.00010+or-0.00026 (95% confidence limits) and mu T=4.15096+or-0.00020+or-0.00037 (99% confidence limits), where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error. This rules out the conjecture mu T+ mu H=6 at the greater than 99% confidence level.

AB - The author uses a recently developed Monte Carlo method to study the connective constant of the self-avoiding walk (SAW) on the triangular lattice. Assuming gamma =43/32 one finds mu T=4.15096+or-0.00010+or-0.00026 (95% confidence limits) and mu T=4.15096+or-0.00020+or-0.00037 (99% confidence limits), where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error. This rules out the conjecture mu T+ mu H=6 at the greater than 99% confidence level.

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Connective constant of the self-avoiding walk on the triangular lattice

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