Data and scripts from: Dynamics around the site percolation threshold on high-dimensional hypercubic lattices

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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 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. ... [Read More]

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6 files (1.19 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
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ARK
  • ark:/87924/r4571cf37
Type
Related Materials
Funding Agency
  • NSF
  • Simons Foundation
Grant Number
  • NSF PHY17-48958
  • Simons Foundation grant #454935, #454937
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