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Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices

dc.contributor.author Charbonneau, Patrick
dc.contributor.author Biroli, Giulio
dc.contributor.author Hu, Yi
dc.date.accessioned 2019-02-05T01:56:07Z
dc.date.available 2019-02-05T01:56:07Z
dc.identifier.uri https://hdl.handle.net/10161/18060
dc.description.abstract 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.
dc.subject cond-mat.stat-mech
dc.subject cond-mat.stat-mech
dc.title Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
dc.type Journal article
dc.date.updated 2019-02-05T01:56:06Z
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Duke
pubs.organisational-group Chemistry
pubs.organisational-group Physics
duke.contributor.orcid Charbonneau, Patrick|0000-0001-7174-0821


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