Eriçok O B, Ganesan K, Mason J K
Materials Science and Engineering, University of California, Davis, California, 95616, USA.
Phys Rev E. 2021 Nov;104(5-2):055304. doi: 10.1103/PhysRevE.104.055304.
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple and could provide valuable information about the nature of phase transitions. Specifically, the topological changes in the configuration space as a function of packing fraction have been conjectured to be related to the onset of first-order phase transitions. The critical configurations for 1 to 12 spheres are sampled using a Morse-theoretic approach, and they are available in an online, interactive database. Explicit triangulations are constructed for the configuration spaces of the two sphere system, and their topological and geometric properties are studied. The critical configurations are found to be associated with geometric changes to the configuration space that connect previously distant regions and reduce the configuration space diameter as measured by the commute time and diffusion distances. The number of such critical configurations around the packing fraction of the solid-liquid phase transition increases exponentially with the number of spheres, suggesting that the onset of the first-order phase transition in the thermodynamic limit is associated with a discontinuity in the configuration space diameter.
硬球系统常被用于对简单流体进行建模。三维环面中硬球在各种对称群作用下的构型空间相对简单，并且能提供有关相变本质的有价值信息。具体而言，构型空间中作为填充率函数的拓扑变化被推测与一级相变的开始有关。使用莫尔斯理论方法对1到12个球体的临界构型进行采样，这些临界构型可在一个在线交互式数据库中获取。为双球系统的构型空间构建了显式三角剖分，并研究了它们的拓扑和几何性质。发现临界构型与构型空间的几何变化相关，这些变化连接了先前遥远的区域，并减小了由通勤时间和扩散距离测量的构型空间直径。在固 - 液相变填充率附近的此类临界构型数量随球体数量呈指数增加，这表明在热力学极限下一级相变的开始与构型空间直径的不连续性有关。
