硬盘模型中粒子均方位移的下界
Lower bound on the mean square displacement of particles in the hard disk model
摘要：
硬盘模型是粒子通过纯硬核排斥相互作用的2D吉布斯过程。在高颗粒密度的模型被认为是显示取向顺序，然而，它是已知的不表现出位置顺序。在这里，我们调查到什么程度粒子的位置可能波动。我们考虑一个有限体积版本的模型在一个盒子的尺寸$2n \times 2n$与任意边界配置，我们表明，颗粒的均方位移的中心附近的盒子是有界的从下面由$c \log n$。结果推广到一大类模型具有相当任意的相互作用。
英文摘要：
The hard disk model is a 2D Gibbsian process of particles interacting via pure hard core repulsion. At high particle density the model is believed to show orientational order, however, it is known not to exhibit positional order. Here we investigate to what extent particle positions may fluctuate. We consider a finite volume version of the model in a box of dimensions $2n \times 2n$ with arbitrary boundary configuration,and we show that the mean square displacement of particles near the center of the box is bounded from below by $c \log n$. The result generalizes to a large class of models with fairly arbitrary interaction.
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