A Rechnitzer and E J Janse van Rensburg 2002 J. Phys. A: Math. Gen. 35 L605 doi:10.1088/0305-4470/35/42/103
Canonical Monte Carlo determination of the connective constant of self-avoiding walks
FREE ARTICLEA Rechnitzer1 and E J Janse van Rensburg2
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We define a statistic an(w), the size of the atmosphere of a self-avoiding walk, w, of length n, with the property that 
an(w)
→ μ as n → ∞, where μ is the growth constant of lattice self-avoiding walks. Both μ and the entropic exponent γ may be estimated to high precision from a(w) using canonical Monte Carlo simulations of self-avoiding walks. Previous Monte Carlo measurements of μ and γ have used grand canonical Monte Carlo simulations. Our simulations indicate that μ → 2.63816 ± 0.00006 and γ = 1.345 ± 0.002. These results, based on a modest computer run, are comparable to the best estimates for μ and γ from (grand canonical) Monte Carlo simulations, and are at most two digits of the best series estimates of μ for self-avoiding walks available in the literature.
- PACS
- MSC
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82C80 Numerical methods (Monte Carlo, series resummation, etc.)
- Subjects
- Dates
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Issue 42 (25 October 2002)
Received 21 August 2002
Published 8 October 2002
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Canonical Monte Carlo determination of the connective constant of self-avoiding walks
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