一种用于干扰的实空间重整化群
A real-space renormalization group for jamming
摘要：
堵塞发生在颗粒材料中，以及在乳液、稠密悬浮液和其他无定形颗粒系统中。当填充分数$ϕ$（定义为颗粒体积与系统体积的比率）增加超过临界值$ϕ_c$时，发生液-固相变，并且晶粒不再能够重新排列。以前的研究表明，$ϕ= ϕ_c$附近的空间相关性发散的证据，但一直没有明确的空间重整化群（RG）计划，已捕捉到这种转变。在这里，我提出了这样一个方案的候选人，使用块自旋一样的随机空出的晶格的颗粒的变换。我定义了一个基于局部机械稳定性的实空间RG变换。该模型显示了一个临界填充分数$ϕ_c$，并给出了二维和三维临界指数的估计。
英文摘要：
Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction $ϕ$, defined as the ratio of particle volume to system volume, is increased past a critical value $ϕ_c$, a liquid-solid phase transition occurs, and grains are no longer able to rearrange. Previous studies have shown evidence of spatial correlations that diverge near $ϕ= ϕ_c$, but there has been no explicit spatial renormalization group (RG) scheme that has captured this transition. Here, I present a candidate for such a scheme, using a block-spin-like transformation of a randomly vacated lattice of grains. I define a real-space RG transformation based on local mechanical stability. This model displays a critical packing fraction $ϕ_c$ and gives estimates of critical exponents in two and three dimensions.
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