Dynamics around the site percolation threshold on high-dimensional hypercubic lattices.

Journal Article (Journal Article)

Recent advances on the glass problem motivate reexamining classical models of percolation. Here we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical dimension of simple percolation, d_{u}=6. Using theory and simulations, we consider the scaling regime and obtain that both caging and subdiffusion scale logarithmically for d≥d_{u}. The theoretical derivation, which considers Bethe lattices with generalized connectivity and a random graph model, confirms that logarithmic scalings should persist in the limit d→∞. The computational validation employs accelerated random walk simulations with a transfer-matrix description of diffusion to evaluate directly the dynamical critical exponents below d_{u} as well as their logarithmic scaling above d_{u}. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.

Full Text

Duke Authors

Cited Authors

  • Biroli, G; Charbonneau, P; Hu, Y

Published Date

  • February 2019

Published In

Volume / Issue

  • 99 / 2-1

Start / End Page

  • 022118 -

PubMed ID

  • 30934351

Electronic International Standard Serial Number (EISSN)

  • 2470-0053

International Standard Serial Number (ISSN)

  • 2470-0045

Digital Object Identifier (DOI)

  • 10.1103/physreve.99.022118


  • eng