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A Fast Monte Carlo Algorithm for Site or Bond Percolation

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  • M. E. J. Newman
  • R. M. Ziff

Abstract

We describe in detail a new and highly effcient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.

Suggested Citation

  • M. E. J. Newman & R. M. Ziff, 2001. "A Fast Monte Carlo Algorithm for Site or Bond Percolation," Working Papers 01-02-010, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:01-02-010
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    Cited by:

    1. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Winkert, Éder & de Oliveira, Paulo M.C. & Faria, Luiz R.R., 2019. "Modeling diploid male dynamics in Hymenoptera: Effects of the number of alleles, dispersal by random walk and simple spatial structuring," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 45-55.
    3. Malarz, Krzysztof, 2023. "Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    4. Huang, Xudong & Yang, Dong & Kang, Zhiqin, 2021. "Impact of pore distribution characteristics on percolation threshold based on site percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    5. D. Dujak & A. Karač & Lj. Budinski-Petković & Z. M. Jakšić & S. B. Vrhovac, 2022. "Percolation and jamming properties in particle shape-controlled seeded growth model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-16, September.
    6. Almeira, Nahuel & Perotti, Juan Ignacio & Chacoma, Andrés & Billoni, Orlando Vito, 2021. "Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Katori, Machiko & Katori, Makoto, 2021. "Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).

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