Simple fluctuations in simple glass formers

TL;DR

This paper investigates critical particle fluctuations in simple glass formers across dimensions, comparing theoretical predictions from MCT and DMFT, and finds that mean-field theory aligns better with simulations in high dimensions.

Contribution

It establishes scaling laws for critical fluctuations in glass formers and compares MCT and DMFT predictions, highlighting the relevance of mean-field theory in finite dimensions.

Findings

DMFT predictions match simulation results in high dimensions

MCT's dimensional scalings are inconsistent with DMFT

Local structure and dimensionality influence fluctuations in complex ways

Abstract

Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways.