一个大包装可以用小包装组装起来吗？
Can a large packing be assembled from smaller ones?
摘要：
我们认为零温度包装软球，经历了一个堵塞到unjumping过渡作为包装分数的函数。我们比较差异的结构，从接触统计，一个大包装的有限子系统，一个整体的包装与周期性的边界的大小和压力相等。我们发现，整体填充系综的涨落小于子系统系综的涨落。这两个量的收敛似乎发生在非常大的系统，这通常是无法实现的数值模拟。发现在二维和三维的包装之间的差异，我们也考虑了四维和平均场模型，并发现他们表现出类似的系统尺寸依赖性。平均场临界指数似乎是一致的3D和4D包装，这表明他们以上的上临界尺寸。我们还发现，作为系统大小的函数的热力学极限的收敛的特点是由两个不同的长度尺度。我们认为，这是由于系统的上临界尺寸以上。
英文摘要：
We consider zero temperature packings of soft spheres, that undergo a jamming to unjamming transition as a function of packing fraction. We compare differences in the structure, as measured from the contact statistics, of a finite subsystem of a large packing to a whole packing with periodic boundaries of an equivalent size and pressure. We find that the fluctuations of the ensemble of whole packings are smaller than those of the ensemble of subsystems. Convergence of these two quantities appears to occur at very large systems, which are usually not attainable in numerical simulations. Finding differences between packings in two dimensions and three dimensions, we also consider four dimensions and mean-field models, and find that they show similar system size dependence. Mean-field critical exponents appear to be consistent with the 3d and 4d packings, suggesting they are above the upper critical dimension. We also find that the convergence as a function of system size to the thermodynamic limit is characterized by two different length scales. We argue that this is the result of the system being above the upper critical dimension.
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