We have studied a class of marginally jammed states in a system of hard disks confined in a narrow channel—a quasi-one-dimensional system—whose exponents are not those predicted by theories valid in the infinite dimensional limit. The exponent $\gamma$ which describes the distribution of small gaps takes the value 1 rather than the infinite dimensional value $0.41269\cdots$. Our work shows that there exist jammed states not found within the tiling approach of Ashwin and Bowles. The most dense of these marginal states is an unusual state of matter that is asymptotically crystalline.

中文翻译：

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一维通道中硬盘的边缘卡死状态

我们研究了在狭窄通道内的硬盘系统（准一维系统）中的一类边缘阻塞状态，其指数不是由在无限维数范围内有效的理论所预测的。指数$\gamma$ 描述小间隙的分布采用值1而不是无穷维值 $0.41269\cdots$。我们的工作表明，在Ashwin和Bowles的平铺方法中没有发现阻塞状态。这些边缘状态中最密集的是渐近结晶的不寻常物质状态。