探索渗流景观：几何相变的无限级联
Exploring Percolative Landscapes: Infinite Cascades of Geometric Phase Transitions
摘要：
许多动力学过程在1+1（时空）维中的演化导致了2d定向分解景观。这些模型的活动相具有许多隐藏的几何顺序，其特征在于我们定义的各种类型的大规模和/或粗粒度渗透主干。对于起源于经典的定向渗流（DP）和接触过程（CP）的图案，我们从蒙特卡罗模拟数据表明，这些分解骨干出现在特定的临界点作为连续相变的结果。这些几何跃迁属于DP普适类，它们的非局部序参量是相应骨架的容量。众多的可想象的分解骨干意味着存在无限级联的这种几何过渡的动力学过程中考虑。我们提出了简单的参数来支持这样的级联过渡的猜想是一个通用的功能，渗流以及许多其他过渡与非本地序参量。
英文摘要：
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2d directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process (CP) we show from the Monte-Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions is a generic feature of percolation as well as many others transitions with nonlocal order parameters.
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