发表机构
Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University; Wuhan Institute of Quantum Technology（教育部人工微纳结构重点实验室与物理科学与技术学院，武汉大学; 武汉量子技术研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过三个硬方形系统，发现构型空间在特征密度下分离，并揭示L形排列偏好，表明排除体积几何在少粒子极限中已能主导结构选择。
AI 中文摘要
具有不同形状的硬粒子的自组装仅通过排除体积约束就能产生丰富的结构多样性。在这里，我们表明，即使是一个由三个硬方形组成的最小系统，被限制在二维周期性盒子中，也表现出与结构选择相关的非平凡构型行为。随着堆积分数的增加，从马尔可夫链蒙特卡洛和均匀非重叠插入采样获得的径向分布函数在低密度下一致，在中间范围内显著偏离，并在更高密度下再次收敛。压力测量提供了强有力的数值证据，表明这种差异源于允许的构型空间在特征密度以上分离成两个不连通的区域。我们将分离密度确定为$\phi_{\rm sep}=3/5$，构造了连接其下方两个区域的显式无重叠转变路径，并量化了它们相对的构型空间体积。在更高的堆积分数下，粒子中心的近似L形排列比交错排列更受青睐，揭示了大硬方形系统中四重和方形晶格有序的特征结构基序。这些结果表明，即使在三粒子系统中，排除体积几何也能同时控制构型连通性和局部结构选择，揭示了许多粒子自组装的迹象如何在少粒子极限中已经出现。
英文摘要
Self-assembly of hard particles with diverse shapes gives rise to a rich variety of structures through excluded-volume constraints alone. Here we show that even a minimal system of three hard squares confined in a two-dimensional periodic box exhibits nontrivial configurational behavior relevant to structure selection. As the packing fraction increases, radial distribution functions obtained from Markov-chain Monte Carlo and uniform non-overlapping insertion sampling agree at low densities, deviate markedly over an intermediate range, and converge again at higher densities. Pressure measurements provide strong numerical evidence that the discrepancy originates from the separation of the allowed configurational space into two disconnected regions above a characteristic density. We identify the separation density as $ϕ_{\rm sep}=3/5$, construct explicit overlap-free transition pathways connecting the two regions immediately below it, and quantify their relative configurational-space volumes. At higher packing fractions, an approximately L-shaped arrangement of the particle centers becomes strongly favored over a staggered one, revealing a structural motif characteristic of tetratic and square-lattice ordering in larger hard-square systems. These results show that excluded-volume geometry can govern both configurational connectivity and local structure selection even in a three-particle system, revealing how signatures of many-particle self-assembly can already emerge in the few-particle limit.
Comments6 pages, 4 figures and Supplemental Material
