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
Pubmed Central 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
Language
- eng