TY - JOUR
T1 - Percolation on infinitely ramified fractal networks
AU - Balankin, Alexander S.
AU - Martínez-Cruz, M. A.
AU - Susarrey-Huerta, O.
AU - Damian Adame, L.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/1/5
Y1 - 2018/1/5
N2 - We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff (DH), topological Hausdorff (DtH), and spectral (ds) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers (DH, DtH, ds), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension DtH, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension DH. The effect of the network connectivity on the site percolation threshold is revealed.
AB - We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff (DH), topological Hausdorff (DtH), and spectral (ds) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers (DH, DtH, ds), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension DtH, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension DH. The effect of the network connectivity on the site percolation threshold is revealed.
KW - Critical exponents
KW - Dimension numbers
KW - Infinitely ramified networks
KW - Percolation
KW - Percolation threshold
KW - Sierpiński carpets
UR - http://www.scopus.com/inward/record.url?scp=85032215367&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2017.10.035
DO - 10.1016/j.physleta.2017.10.035
M3 - Artículo
SN - 0375-9601
VL - 382
SP - 12
EP - 19
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1
ER -