Physics Research Institute, Southern Federal University, 344090, Stachki 194, Rostov-on-Don, Russia.
Department of Physics, Laurentian University, Sudbury, Ontario, Canada P3E 2C6.
Phys Rev E. 2016 Jan;93(1):012102. doi: 10.1103/PhysRevE.93.012102. Epub 2016 Jan 6.
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 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 are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
在 1+1（时空）维度中，许多动力学过程的演化导致了 2D 有向渗滤景观。这些模型的活跃相具有许多隐藏的几何顺序，其特征是各种类型的大规模和/或粗粒度的渗滤骨干，我们定义了这些骨干。对于源于经典有向渗流（DP）和接触过程的模式，我们从蒙特卡罗模拟数据中表明，这些渗滤骨干在特定的临界点作为连续相变的结果而出现。这些几何转变属于 DP 普遍性类别，它们的非局部序参量是相应骨干的容量。可以想象的众多渗滤骨干意味着在所考虑的动力学过程中存在无限级联的这种几何转变。我们提出了简单的论据来支持这样的假设，即这种转变的级联是渗滤以及具有非局部序参量的许多其他转变的通用特征。
