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The Gaussian model of explosive percolation in three and higher dimensions | K. J. Schrenk
; N. A. M. Araújo
; H. J. Herrmann
; | Date: |
28 Apr 2011 | Abstract: | The Gaussian model of explosive percolation, recently introduced by Ara’ujo
and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically
investigated in three dimensions, disclosing a discontinuous transition. For
the simple-cubic lattice, in the thermodynamic limit, we report a finite jump
of the order parameter, J=0.415 +/- 0.005. The largest cluster at the threshold
is compact, but its external perimeter is fractal with fractal dimension d_A =
2.5 +/- 0.2. The study is extended to hypercubic lattices up-to six dimensions
and to the mean-field limit (infinite dimension). We find that, in all
considered dimensions, the percolation transition is discontinuous. The value
of the jump in the order parameter, the maximum of the second moment, and the
percolation threshold are analyzed, revealing interesting features of the
transition and corroborating its discontinuous nature in all considered
dimensions. We also show that the fractal dimension of the external perimeter,
for any dimension, is consistent with the one from bridge percolation and
establish a lower bound for the percolation threshold of discontinuous models
with finite number of clusters at the threshold. | Source: | arXiv, 1104.5376 | Services: | Forum | Review | PDF | Favorites |
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