发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出平移有序度量τ_T及其键取向类似物τ_O，统一量化多粒子系统有序性，并应用于平衡硬粒子、RSA堆积和隐形超均匀系统，揭示结构有序性的制备依赖性和正相关关系。
AI 中文摘要
量化多粒子系统中的有序/无序程度仍然是物理学、材料科学和数学中的一个突出问题。为此，我们考虑了平移有序度量 $\tau_T$，定义为总关联函数 $h(\mathbf{r})$ 的 $L^2$ 范数的平方，并引入其键取向类似物 $\tau_O$，该度量基于使用局部取向权重的加权总关联函数 $h_{\mathbf{f}}(\mathbf{r})$（S. Torquato 等人，Phys. Rev. X 16, 011042 (2026)）。配对 $(\tau_T,\tau_O)$ 将两种形式的有序性置于共同的两点统计基础上。我们计算了二维和三维中两种非超均匀球堆积模型在堆积分数 $\phi$ 函数下的这两个度量：1) 平衡硬粒子系统和 2) 非平衡随机顺序添加（RSA）堆积。对于非超均匀系统，在平衡流体和 RSA 构型中，键取向有序性保持次主导地位；然而，其相对于平移度量的幅度在平衡流体分支的上端附近增加，在二维中比在三维中强得多，并且在采样的晶体分支上，这两个度量变得相当。在共同的堆积分数下，平衡流体和 RSA 堆积描绘出不同的 $(\tau_T,\tau_O)$ 轨迹，揭示了依赖于制备过程的结构有序性差异。作为一个代表性的超均匀家族，我们研究了 $0<\chi<1/2$ 的二维无序隐形超均匀（SHU）基态，其中 $\chi$ 是隐形参数。在无序 SHU 相内，键取向有序性保持次主导地位，但其相对于平移度量的幅度向无序-有序阈值方向增加。在所有三个模型中，$\tau_T$ 和 $\tau_O$ 在泊松参考区域之外呈正相关：在所采样的状态点上，$\tau_O$ 随 $\tau_T$ 单调增加。
英文摘要
Quantifying the degree of order/disorder in many-particle systems remains an outstanding problem in physics, materials science, and mathematics. To this end, we consider the translational order metric $τ_T$, defined as the squared $L^2$ norm of the total correlation function $h(\mathbf{r})$, and introduce its bond-orientational analogue $τ_O$, defined from the weighted total correlation function $h_{\mathbf{f}}(\mathbf{r})$ using local orientational weights (S. Torquato et al., Phys. Rev. X 16, 011042 (2026)). The pair $(τ_T,τ_O)$ places both forms of order on a common two-point statistical footing. We compute both metrics for two nonhyperuniform sphere-packing models in 2D and 3D as functions of packing fraction $ϕ$: 1) equilibrium hard particles and 2) nonequilibrium random sequential addition (RSA) packings. For the nonhyperuniform systems, bond-orientational order remains subdominant along the equilibrium-fluid and RSA configurations; however, its magnitude relative to the translational metric increases near the upper end of the equilibrium-fluid branches, much more strongly in 2D than in 3D, and the two metrics become comparable along the sampled crystal branches. At common packing fractions, equilibrium fluids and RSA packings trace distinct $(τ_T,τ_O)$ trajectories, revealing preparation-dependent differences in structural order. As a representative hyperuniform family, we study 2D disordered stealthy hyperuniform (SHU) ground states for $0<χ<1/2$, where $χ$ is the stealthiness parameter. Within the disordered SHU phase, bond-orientational order remains subdominant, but its magnitude relative to the translational metric increases toward the disorder-to-order threshold. In all three models, $τ_T$ and $τ_O$ are positively correlated beyond the Poisson-reference regime: $τ_O$ increases monotonically with $τ_T$ across the sampled state points.
Comments17 pages, 24 figures
