AI 中文总结
本文重访玻璃化转变的高维理论，通过广义复制液体理论描述粒子级复制体不匹配，应用于高维硬球和谐波球，揭示转变的算法解释并修正传统理论的转变点。
AI 中文摘要
复制液体理论通过将液体的密度泛函理论与最初为自旋玻璃开发的复制方法相结合，为玻璃化转变提供了微观平均场描述。在传统的复制液体理论中，玻璃态的描述假设不同复制体中的粒子围绕共同质心进行振动运动，从而形成包含每个复制体中一个粒子的分子。本文通过允许每个分子仅包含复制体的一个子集，重新审视这一假设。这种广义表述描述了粒子级的复制体不匹配，可能与粒子跳跃等非振动运动相关。我们将该理论应用于高维硬球和谐波球，此处平均场描述预计将变得精确。对于硬球，复制体不匹配会使玻璃亚稳态失稳，并将动力学转变移至显著更高的堆积分数，同时保持主导的热力学玻璃转变不变。所得的转变密度在高维主导阶上与Campos、Jenssen、Michelen和Sahasrabudhe通过离散化版本的贪心随机顺序吸收法获得的随机球堆积的近期严格下界一致，暗示了转变的算法解释：在高维空间中，巨正则动力学比正则动力学更高效。对于有限温度下的谐波球，即使在热力学理想玻璃转变处，玻璃态也包含有限的复制体不匹配分数，从而将转变点从传统复制假设预测的位置偏移。
英文摘要
The replicated liquid theory provides a microscopic mean-field description of the glass transition by combining the density functional theory of liquids with the replica method originally developed for spin glasses. In the conventional replica liquid theory, a glassy state is described by assuming that particles in different replicas undergo vibrational motion around common centers of mass, thereby forming molecules that contain one particle from every replica. Here we revisit this assumption by allowing each molecule to contain only a subset of replicas. This generalized formulation describes particle-level replica mismatches, which may be associated with non-vibrational motions such as particle hopping. We apply the theory to high-dimensional hard and harmonic spheres, where the mean-field description is expected to become exact. For hard spheres, replica mismatches destabilize the glassy metastable state and shift the dynamical transition to a significantly higher packing fraction, while leaving the leading thermodynamic glass transition unchanged. The resulting transition density agrees, at leading order in high dimensions, with the recent rigorous lower bound for random sphere packings obtained by Campos, Jenssen, Michelen, and Sahasrabudhe by using a discretized version of greedy Random Sequential Absorption, suggesting an algorithmic interpretation of the transition: grandcanonical dynamics is more efficient in high dimensional spaces than canonical one. For harmonic spheres at finite temperature, the glassy state contains a finite replica-mismatch fraction even at the thermodynamic ideal-glass transition, thereby shifting the transition point from that predicted by the conventional replica ansatz.
Comments27 pages, 6 figures
