Data from: Finite-dimensional vestige of spinodal criticality above the dynamical glass transition

Finite-dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite-dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalize configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from d = 3 to d = 10. We observe a strong softening of the mean-field square-root singularity in d = 3 that is progressively restored as d increases above d = 8, in surprisingly good agreement with perturbation theory.

旋节线临界性（spinodal criticality）的有限维特征素来以难以获取而闻名。由模耦合理论（mode-coupling theory）首次提出的玻璃形成液体动力学转变，本质是一种旋节线不稳定性，该不稳定性会被热激活过程抑制，而热激活过程同时也限制了体系能趋近该不稳定性的程度。我们结合多种数值手段，直接观测到了有限维玻璃形成体系中旋节线临界性的残存特征。我们采用交换蒙特卡洛算法（swap Monte Carlo algorithm），对超过模耦合交叉点的体系构型进行高效热化，并通过一套剔除热激活过程的分析方案，对空间维度d=3至d=10范围内的体系动力学进行了研究。我们观测到，在d=3时，平均场平方根奇异性出现了显著软化，且随着维度升高至d=8以上，该软化效应会逐渐被恢复，这一结果与微扰理论（perturbation theory）的预测有着惊人的良好契合度。