论文标题
缩放预成分的平均场预测匹配低维困扰的包装
Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings
论文作者
论文摘要
没有已知的分析框架准确地解释了在干扰中观察到的所有现象。玻璃和干扰的副本理论是一种平均野外理论，它试图通过在无限维度的极限下进行工作，从而使邻居之间的相关性可忽略不计。因此，在有限的维度中不能保证这种平均场理论的结果。但是，在低维度中，许多均值的均值结果被证明是精确或几乎精确的。这表明无需尺寸限制即可获得这些结果。在本文中，我们对压力，多余的填充分数和从维度2-10的多余接触数量之间的缩放缩放关系进行精确测量，以便将预成型物提取到这些尺度上。尽管这些预成分应对有限维校正高度敏感，但我们发现这些预成分的平均场预测在低维度中是确切的。因此，平均场近似对于得出这些预成分是不需要的。我们提出了一个确切的第一原理派生，将另一个作为一个悬而未决的问题。
No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glass and jamming is a mean field theory which attempts to do so by working in the limit of infinite dimensions, such that correlations between neighbors are negligible. As such, results from this mean field theory are not guaranteed to be observed in finite dimensions. However, many results in mean field for jamming have been shown to be exact or nearly exact in low dimensions. This suggests that the infinite dimensional limit is not necessary to obtain these results. In this paper, we perform precision measurements of jamming scaling relationships between pressure, excess packing fraction, and number of excess contacts from dimensions 2-10 in order to extract the prefactors to these scalings. While these prefactors should be highly sensitive to finite dimensional corrections, we find the mean field predictions for these prefactors to be exact in low dimensions. Thus the mean field approximation is not necessary for deriving these prefactors. We present an exact, first principles derivation for one, leaving the other as an open question.
