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2
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0004081447
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Princeton University Press, Princeton, NJ
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D. J. Watts, Small Worlds (Princeton University Press, Princeton, NJ, 1999).
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(1999)
Small Worlds
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Watts, D.J.1
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8
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85036147965
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Phys. Rev. E (to be published)
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C. Moukarzel, Phys. Rev. E (to be published).
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Moukarzel, C.1
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10
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85036320475
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Technically this point is not a percolation transition, since it is not possible to create a system-spanning (i.e., percolating) cluster on a small-world graph. To be strictly correct, we should refer to the transition as “the point at which a giant component first forms.” This is something of a mouthful, however, so we will bend the rules a little and continue to talk about “percolation” in this paper
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Technically this point is not a percolation transition, since it is not possible to create a system-spanning (i.e., percolating) cluster on a small-world graph. To be strictly correct, we should refer to the transition as “the point at which a giant component first forms.” This is something of a mouthful, however, so we will bend the rules a little and continue to talk about “percolation” in this paper.
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11
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0003919678
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D. Ferguson, J. I. Siepmann, D. G. Truhlar, Wiley, New York
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G. T. Barkema and M. E. J. Newman, in Monte Carlo Methods in Chemical Physics, edited by D. Ferguson, J. I. Siepmann, and D. G. Truhlar (Wiley, New York, 1999).
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(1999)
Monte Carlo Methods in Chemical Physics
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Barkema, G.T.1
Newman, M.E.J.2
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12
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85036265176
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We have also experimented with finite-size scaling as a method for calculating (Formula presented) Such calculations are, however, prone to inaccuracy because, as pointed out in Ref. 7, the correlation length scaling exponent (Formula presented), which governs the behavior of (Formula presented) as system size is varied, depends on the effective dimension of the graph, which itself changes with system size. Thus the exponent can at best be considered only approximately constant in a finite-size scaling calculation. Rather than introduce unknown errors into the value of (Formula presented) as a result of this approximation, we have opted in the present work to quote direct measurements of (Formula presented) on large systems as our best estimate of the percolation threshold
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We have also experimented with finite-size scaling as a method for calculating (Formula presented) Such calculations are, however, prone to inaccuracy because, as pointed out in Ref. 7, the correlation length scaling exponent (Formula presented), which governs the behavior of (Formula presented) as system size is varied, depends on the effective dimension of the graph, which itself changes with system size. Thus the exponent can at best be considered only approximately constant in a finite-size scaling calculation. Rather than introduce unknown errors into the value of (Formula presented) as a result of this approximation, we have opted in the present work to quote direct measurements of (Formula presented) on large systems as our best estimate of the percolation threshold.
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