Data from: Simple fluctuations in simple glass formers

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 sphere fluids 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.

与粒子位移相关的临界单粒子涨落，是大维度极限下简单玻璃形成液体的固有属性，并会在所有有限维度中留下准临界痕迹。这一特征可作为区分玻璃化转变理论的关键判据。本文针对硬球液体与最简结构马里-库尔恰恩（Mari-Kurchan）模型，在不同维度下分别基于模式耦合理论（mode-coupling theory, MCT）与动力学平均场理论（dynamical mean-field theory, DMFT），通过被广泛认可的非高斯参数对上述临界涨落进行表征并展开研究。本文推导了适用于大维度下任意液体动力学理论的普适标度律，并证明模式耦合理论所预测的维度标度行为与动力学平均场理论的结果并不一致。中等偏高维度下硬球流体的模拟结果与动力学平均场理论的理论图景相符，进一步验证了平均场理论在有限维度下描述玻璃态物理的合理性。本文提出了可对模式耦合理论进行修正的潜在可行方向，以兼容部分平均场物理特性。本研究同时表明，局域结构与空间维度会以非平凡的方式对单粒子临界涨落产生影响。