- 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 part, and obtain that both caging and subdiffusion scale logarithmically for d >= d_u. The theoretical derivation considers Bethe lattices with generalized connectivity and a random graph model, and employs a scaling analysis to confirm that logarithmic scalings should persist in the infinite dimension limit. The computational validation employs accelerated random walk simulations with a ... [Read More]
- Total Size
- 3 files (1.18 MB)
- Data Citation
- Birolo, G., Charbonneau, P., & Hu, Y. (2019). Data and scripts from: Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices. Duke Digital Repository. https://doi.org/10.7924/r4571cf37
- DOI
- 10.7924/r4571cf37
- Publication Date
- February 5, 2019
- ARK
- ark:/87924/r4571cf37
- Affiliation
- Publisher
- Type
- Related Materials
- Funding Agency
- NSF
- Simons Foundation
- Grant Number
- NSF PHY17-48958
- Simons Foundation grant #454935, #454937
- Contact
- Yi Hu: yi.hu@duke.edu
- Title
- Data and scripts from: Dynamics around the site percolation threshold on high-dimensional hypercubic lattices
- Repository
