Publications [#341477] of Patrick Charbonneau

Papers Published

1. Biroli, G; Charbonneau, P; Hu, Y, Dynamics around the site percolation threshold on high-dimensional hypercubic lattices., Physical review. E, vol. 99 no. 2-1 (February, 2019), pp. 022118 [doi]
   (last updated on 2024/04/23)

   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 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.