Artikel,

Gaussian model of explosive percolation in three and higher dimensions

, , und .
PHYSICAL REVIEW E, (2011)
DOI: 10.1103/PhysRevE.84.041136

Zusammenfassung

The Gaussian model of discontinuous percolation, recently introduced by Araujo 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 a finite number of clusters at the threshold.

Tags

Nutzer

  • @nonancourt
  • @ppgfis_ufc_br

Kommentare und Rezensionen