Mean-Field Caging in a Random Lorentz Gas

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