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Phase transitions in the node, edge, bootstrap, and diffusion percolation models on the Sierpiński carpet

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  • Jang, Hoseung
  • Yu, Unjong

Abstract

We investigate four types of percolation models — node, edge, bootstrap, and diffusion percolation — in three fractal graphs constructed on the Sierpiński carpet, employing the Monte Carlo method based on the Newman–Ziff algorithm. For each case, we calculate the percolation threshold and critical exponents (ν, γ, and β) through the crossing of percolation probabilities and the finite-size scaling analysis, incorporating correction-to-scaling effects. Our results reveal that critical exponents of the percolation phase transition in the three fractal graphs exhibit universality across all four percolation models. Furthermore, we demonstrate that the hyperscaling relation dν=γ+2β is also valid in the percolation phase transition on the Sierpiński carpet if the spatial dimension d is replaced by the Hausdorff dimension.

Suggested Citation

  • Jang, Hoseung & Yu, Unjong, 2024. "Phase transitions in the node, edge, bootstrap, and diffusion percolation models on the Sierpiński carpet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 655(C).
    • Handle: RePEc:eee:phsmap:v:655:y:2024:i:c:s0378437124006733
    DOI: 10.1016/j.physa.2024.130164
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    References listed on IDEAS

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    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
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    3. N. S. Branco & Cristiano J. Silva, 1999. "UNIVERSALITY CLASS FOR BOOTSTRAP PERCOLATION WITHm=3ON THE CUBIC LATTICE," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 921-930.
    4. Yu, Unjong, 2015. "Critical temperature of the Ising ferromagnet on the fcc, hcp, and dhcp lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 75-79.
    5. P. M. Centres & F. Nieto, 2024. "Determination of the non-Euclidean lower critical dimension for the site percolation problem," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-11, July.
    6. Jang, Hoseung & Yu, Unjong, 2019. "Universality class of the percolation in two-dimensional lattices with distortion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
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