软核模型中的反直觉基态
Counterintuitive ground states in soft-core models
摘要：
众所周知，统计力学系统在高维空间表现出微妙的行为。在本文中，我们表明，某些自然的软核模型，如高斯核模型，有意想不到的复杂的基态，即使在相对较低的维度。具体地说，我们反驳了Torquato和Stillinger的一个猜想，他们预测2到8维的高斯核模型的稀基态将是布拉维晶格。我们证明了在5维和7维中，实际上存在较低能量的非布拉维晶格。(The最接近的三维类似物是六方密堆积，但它具有比面心立方晶格更高的能量。我们相信这些现象实际上是相当普遍的，并且我们将它们与高维中的去相关联系起来。
英文摘要：
It is well known that statistical mechanics systems exhibit subtle behavior in high dimensions. In this paper, we show that certain natural soft-core models, such as the Gaussian core model, have unexpectedly complex ground states even in relatively low dimensions. Specifically, we disprove a conjecture of Torquato and Stillinger, who predicted that dilute ground states of the Gaussian core model in dimensions 2 through 8 would be Bravais lattices. We show that in dimensions 5 and 7, there are in fact lower-energy non-Bravais lattices. (The nearest three-dimensional analog is the hexagonal close-packing, but it has higher energy than the face-centered cubic lattice.) We believe these phenomena are in fact quite widespread, and we relate them to decorrelation in high dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
