论文标题
FA-2F动力学限制模型的急剧阈值
Sharp threshold for the FA-2f kinetically constrained model
论文作者
论文摘要
Fredrickson-Andersen 2-Spin促进了$ \ Mathbb {Z}^D $（FA-2F）上的模型，是一种具有动力学促进（KCM）的范式相互作用的粒子系统，具有动力学促进，这是凝结物理学的重要机制。在FA-2F中，仅当至少两个最近的邻居空着时，一个站点才能改变其状态。尽管该过程是可逆的W.R.T.产品的伯努利度量，它没有吸引力，并且具有变性的跳跃速率和特征时间尺度的异常差异，因为空站点的密度$ q $往往$ 0 $。编码上述功能的自然随机变量是$τ_0$，这是第一次为固定过程源变为空的。我们的主要结果是尖锐的阈值\ [τ_0= \ exp \ big（\ frac {d \cdotλ（d，2）+o（d，2）+o（1）} {q^{1/（d-1/（d-1）} \ big）\ quad \ quad \ quad \ fext {w.h.p。 $ \ Mathbb {z}^d $上的渗透，单调确定性自动机的FA-2F对应物。这是关键KCM的第一个尖锐结果，它与Holroyd在2003年的自举渗透及其随后的改进相比。在过去的四十年中，它还解决了物理文献中积累的各种争议。此外，我们的新技术可以完成有关关键KCM的近期雄心勃勃的雄心勃勃的计划，并为其他二维KCM建立尖锐的阈值。
The Fredrickson-Andersen 2-spin facilitated model on $\mathbb{Z}^d$ (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics. In FA-2f a site may change its state only if at least two of its nearest neighbours are empty. Although the process is reversible w.r.t. a product Bernoulli measure, it is not attractive and features degenerate jump rates and anomalous divergence of characteristic time scales as the density $q$ of empty sites tends to $0$. A natural random variable encoding the above features is $τ_0$, the first time at which the origin becomes empty for the stationary process. Our main result is the sharp threshold \[τ_0=\exp\Big(\frac{d\cdotλ(d,2)+o(1)}{q^{1/(d-1)}}\Big)\quad \text{w.h.p.}\] with $λ(d,2)$ the sharp threshold constant for 2-neighbour bootstrap percolation on $\mathbb{Z}^d$, the monotone deterministic automaton counterpart of FA-2f. This is the first sharp result for a critical KCM and it compares with Holroyd's 2003 result on bootstrap percolation and its subsequent improvements. It also settles various controversies accumulated in the physics literature over the last four decades. Furthermore, our novel techniques enable completing the recent ambitious program on the universality phenomenon for critical KCM and establishing sharp thresholds for other two-dimensional KCM.
