• DOI:10.1103/PhysRevE.104.024137
• Corpus ID: 234357912

High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas.

@article{Charbonneau2021HighdimensionalPC,
  title={High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas.},
  author={Benoit Charbonneau and Patrick Charbonneau and Yi Hu and Zhen Yang},
  journal={Physical review. E},
  year={2021},
  volume={104 2-1},
  pages={
          024137
        }
}

• B. Charbonneau, P. Charbonneau, +1 author Zhen Yang
• Published 10 May 2021
• Physics
• Physical review. E

The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization transition at the void percolation threshold is not well controlled analytically nor computationally. A recent study [Biroli et al., Phys. Rev. E 103, L030104 (2021)2470-004510.1103/PhysRevE.103.L030104] of the caging behavior of the RLG motivated by the mean-field theory of glasses has uncovered physical inconsistencies in that scaling that heighten the need for guidance. Here we first extend analytical expectations for asymptotic high-d bounds on the void percolation threshold and then computationally evaluate both the threshold and its criticality in various d. In high-d systems, we observe that the standard percolation physics is complemented by a dynamical slowdown of the tracer dynamics reminiscent of mean-field caging. A simple modification of the RLG is found to bring the interplay between percolation and mean-field-like caging down to d=3.