Counterintuitive ground states in soft-core models

被引:15
作者
Cohn, Henry [1 ]
Kumar, Abhinav [2 ]
机构
[1] Microsoft Res New England, Cambridge, MA 02142 USA
[2] MIT, Dept Math, Cambridge, MA 02139 USA
来源
PHYSICAL REVIEW E | 2008年 / 78卷 / 06期
基金
美国国家科学基金会;
关键词
Gaussian processes; ground states; lattice dynamics; statistical mechanics;
D O I
10.1103/PhysRevE.78.061113
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
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.
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页数:7
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