Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings

被引:10
作者
Sartor, James D. [1 ,2 ]
Ridout, Sean A. [3 ]
Corwin, Eric, I [1 ,2 ]
机构
[1] Univ Oregon, Dept Phys, Eugene, OR 97403 USA
[2] Univ Oregon, Inst Mat Sci, Eugene, OR 97403 USA
[3] Univ Penn, Dept Phys & Astron, Philadelphia, PA 19104 USA
基金
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词
34;
D O I
10.1103/PhysRevLett.126.048001
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glasses 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 Letter, 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, fast-principles derivation for one, leaving the other as an open question. Our results suggest that mean-field theories of critical phenomena may compute more for d >= d(u) than has been previously appreciated.
引用
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页数:5
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