Simple Fluctuations\nin Simple Glass Formers

Critical single-particle fluctuations associated with\nparticle\ndisplacements are inherent to simple glass-forming liquids in the\nlimit of large dimensions and leave a pseudocritical trace across\nall finite dimensions. This characteristic could serve as a crucial\ntest for distinguishing between theories of glass formation. We here\nexamine these critical fluctuations, as captured by the well-established\nnon-Gaussian parameter, within both mode-coupling theory (MCT) and\ndynamical mean-field theory (DMFT) across dimensions for hard sphere\nfluids and for the minimally structured Mari–Kurchan model.\nWe establish general scaling laws relevant to any liquid dynamics\ntheory in large dimensions and show that the dimensional scalings\npredicted by MCT are inconsistent with those from DMFT. Simulation\nresults for hard sphere fluids in moderately high dimensions align\nwith the DMFT scenario, reinforcing the relevance of mean-field theory\nfor capturing glass physics in finite dimensions. We identify potential\nadjustments to MCT to account for certain mean-field physics. Our\nfindings also highlight that local structure and spatial dimensionality\ncan affect single-particle critical fluctuations in nontrivial ways.