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

TL;DR

This paper investigates the high-dimensional behavior of the random Lorentz gas, revealing mean-field-like caging phenomena and providing analytical bounds and computational results on the void percolation transition.

Contribution

It extends analytical bounds for the percolation threshold in high dimensions and demonstrates the emergence of mean-field caging effects at lower dimensions.

Findings

High-dimensional bounds on the void percolation threshold

Observation of mean-field-like caging in high dimensions

Modified RLG model shows caging effects down to d=3

Abstract

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 L030104 (2021)] 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.