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Determination of the non-Euclidean lower critical dimension for the site percolation problem

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  • P. M. Centres

    (Universidad Nacional de San Luis, Instituto de Fisica Aplicada San Luis: “Dr. Giorgio Zgrablich” (INFAP), CONICET
    Universidad Nacional de San Juan, Dpto de Geofísica y Astronomía)

  • F. Nieto

    (Universidad Nacional de San Luis, Instituto de Fisica Aplicada San Luis: “Dr. Giorgio Zgrablich” (INFAP), CONICET)

Abstract

The investigation of site percolation on Sierpinski carpets is carried out through comprehensive numerical simulations. We utilize finite- size scaling theory, staying within the constraints of our computational resources, to determine critical exponents and percolation thresholds. Moreover, we employ an approach developed by Elliot et al. (Phys Rev C 6:3185, 1994; Phys Rev C 55:1319, 1997), which streamlines the process by eliminating the necessity of dealing with large lattices. This method facilitates the extraction of critical quantities that characterize the transition from a single generation within a given structure. By implementing this procedure, we enhance efficiency and accuracy in analyzing the percolation phenomenon on Sierpinski carpets. The obtained values of the percolation thresholds are plotted as a function of the fractal dimensions in order to determine the lower critical dimension of the site percolation problem which is calculated to be $$d_c^L=1.52$$ d c L = 1.52 . In addition, the behavior of the critical exponents as a function of the fractal dimension is also shown and discussed. Graphical abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:7:d:10.1140_epjb_s10051-024-00753-w
    DOI: 10.1140/epjb/s10051-024-00753-w
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