Mean-Field Caging in a Random Lorentz Gas.

Journal Article (Journal Article)

The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, d → ∞ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that, as d increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite-d perturbative and nonperturbative (instantonic) corrections [Biroli et al. Phys. Rev. E 2021, 103, L030104]. Here, we expand on the d → ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/d correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that, although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the d → ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.

Full Text

Duke Authors

Cited Authors

  • Biroli, G; Charbonneau, P; Hu, Y; Ikeda, H; Szamel, G; Zamponi, F

Published Date

  • June 7, 2021

Published In

Volume / Issue

  • 125 / 23

Start / End Page

  • 6244 - 6254

PubMed ID

  • 34096720

Electronic International Standard Serial Number (EISSN)

  • 1520-5207

International Standard Serial Number (ISSN)

  • 1520-6106

Digital Object Identifier (DOI)

  • 10.1021/acs.jpcb.1c02067


  • eng