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

P. M. Centres () and F. Nieto ()
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P. M. Centres: Universidad Nacional de San Luis, Instituto de Fisica Aplicada San Luis: “Dr. Giorgio Zgrablich” (INFAP), CONICET
F. Nieto: Universidad Nacional de San Luis, Instituto de Fisica Aplicada San Luis: “Dr. Giorgio Zgrablich” (INFAP), CONICET

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 7, 1-11

Abstract: 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

Date: 2024
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DOI: 10.1140/epjb/s10051-024-00753-w

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