Special CPM Seminar

Appearance of Multiple Percolative Patterns via Cascades of Geometric Transitions

Gennady Y. Chitov

Department of Physics
Laurentian University

The evolution of many kinetic processes in 1+1 dimensions results in 2D directed percolative landscapes. The active phases of those models possess numerous hidden geometric orders characterized by distinct percolative patterns. From Monte-Carlo simulations of the directed percolation (DP) and the contact process (CP) we demonstrate the emergence of those patterns 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 ordering patterns implies the existence of infinite cascades of such 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 other transitions with non-local order parameters.