Data from: Thermodynamic stability of hard sphere crystals in dimensions 3 through 10

Although much is known about the metastable liquid branch of hard spheres--from low dimension d up to the infinite dimensional limit--its crystal counterpart remains largely unexplored for d>3. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to d=10, and the dimensional trends suggest that crystal stability likely persists well beyond that point.

尽管学界已对硬球（hard spheres）的亚稳液相分支——从低维度d直至无穷维极限——形成了较为充分的认知，但其对应的晶体相在d>3的维度范围内仍未得到充分探索。具体而言，目前仍无法明确晶体相在高维度下是否具备热力学稳定性，进而也难以判定晶体的平均场理论（mean-field theory）是否能够严格成立。为厘清硬球晶体的稳定范围，本文通过数值模拟估算其状态方程，并采用广义Frenkel-Ladd方案计算绝对晶体自由能，以此确定液-晶共存条件。研究结果显示，晶体相至少在d=10时仍保持热力学稳定，且维度演化趋势表明，晶体稳定性极有可能在更高维度下持续存在。