Site percolation on the Penrose rhomb lattice

Ziff, Robert M.; Babalievski, F.

doi:10.1016/s0378-4371(99)00166-1

Cited by 10 publications

(18 citation statements)

References 28 publications

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“…The data collapses for both Penrose and Ammann-Beenker lattices are a strong evidence that the system falls into dynamic percolation universality class in the same way of 2D square lattice [6,7]. Therefore the quasiperiodic order is irrelevant, in agreement with results for classical percolation in the same quasiperiodic lattices [41][42][43].…”

Section: Resultssupporting

confidence: 76%

Epidemic outbreaks on two-dimensional quasiperiodic lattices

Santos

Alves

et al. 2020

Physics Letters A

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We considered the Asynchronous SIR (susceptible-infected-removed) model on Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical behavior by using Newman-Ziff algorithm to track cluster propagation by making a tree structure of clusters grown at the dynamics, allowing to simulate SIR model on non-periodic lattices and measure any observable related to percolation. We numerically calculated the order parameter, defined in a geographical fashion by distinguish between an epidemic state, characterized by a spanning cluster formed by the removed nodes and the endemic state, where there is no spanning cluster. We obtained the averaged mean cluster size which plays the role of a susceptibility, and a cumulant ratio defined for percolation to estimate the epidemic threshold. Our numerical results suggest that the system falls into twodimensional dynamic percolation universality class and the quasiperiodic order is irrelevant, in according to results for classical percolation.PACS numbers:

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Section: Resultssupporting

confidence: 76%

Epidemic outbreaks on two-dimensional quasiperiodic lattices

Santos

Alves

et al. 2020

Physics Letters A

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“…The largely improved estimate of d f is the main focus of our numerical study, rather than obtaining the corrections with precision. We cross check the obtained results with a careful analysis of the local logarithmic slopes as suggested by Ziff [40,41]. This method uses the fact that for large enough system sizes the higher order terms are negligible, such that the local logarithmic slope of the corrections to scaling should converge to the leading correction exponent.…”

Section: Introductionmentioning

confidence: 99%

Corrections to scaling for watersheds, optimal path cracks, and bridge lines

et al. 2012

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We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions (2D and 3D). We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, d(f) =1.2168 ± 0.0005 in 2D and d(f) = 2.487 ± 0.003 in 3D, and the same exponent of the leading correction, Ω = 0.9 ± 0.1 and Ω=1.0 ± 0.1, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and bridge lines are further supported by either heuristic or exact arguments.

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“…Also, ω = 1.2(2) was found by Normand, Herrmann and Hajjar [27] for percolation conductivity on a cylindrical geometry, which may share the same finite-size corrections. In more recent work, Ziff and Babalievski [18] * rziff@umich.edu…”

mentioning

confidence: 99%

“…(Note: there was a minus sign missing in the label of the vertical axis in Ref. [18].) The two lower curves are new plots for bond percolation on the square and triangular lattices, using s0 = 0.25 and 0.5, respectively.…”

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Correction-to-scaling exponent for two-dimensional percolation

Ziff

2011

Phys. Rev. E

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We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Ω ≤ 72/91, ω = DΩ ≤ 3/2, and ∆1 = νω ≤ 2, based upon Cardy's result for the critical crossing probability on an annulus. The upper bounds are consistent with many previous measurements of site percolation on square and triangular lattices, and new measurements for bond percolation presented here, suggesting this result is exact. A scaling form evidently applicable to site percolation is also found.

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Site percolation on the Penrose rhomb lattice

Cited by 10 publications

References 28 publications

Epidemic outbreaks on two-dimensional quasiperiodic lattices

Epidemic outbreaks on two-dimensional quasiperiodic lattices

Corrections to scaling for watersheds, optimal path cracks, and bridge lines

Correction-to-scaling exponent for two-dimensional percolation

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