https://doi.org/10.1140/epjb/s10051-024-00753-w
Regular Article - Statistical and Nonlinear Physics
Determination of the non-Euclidean lower critical dimension for the site percolation problem
1
Departamento de Física, Universidad Nacional de San Luis, Instituto de Fisica Aplicada San Luis: “Dr. Giorgio Zgrablich” (INFAP), CONICET, Ejercito de Los Andes 950, D5700HHW, San Luis, Argentina
2
Universidad Nacional de San Juan, Dpto de Geofísica y Astronomía, Mitre 396 (E), San Juan, J5402CWH, San Juan, Argentina
Received:
14
March
2024
Accepted:
15
July
2024
Published online:
27
July
2024
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 
. In addition, the behavior of the critical exponents as a function of the fractal dimension is also shown and discussed.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
