Hierarchy of percolation patterns in a kinetic replication model

TL;DR

This study uses Monte Carlo simulations and finite-size scaling to explore the hierarchical structure of percolation patterns in a one-dimensional kinetic contact process, revealing multiple phases and continuous transitions within the active phase.

Contribution

It uncovers the hierarchical organization of percolation patterns and extends the Janssen-Grassberger conjecture to multiple percolating phases.

Findings

Five distinct percolation phases identified.

All phase transitions belong to the directed percolation universality class.

Hierarchical cascade of percolation patterns observed.

Abstract

The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the active phase and the nature of transitions those patterns emerge through. Our results corroborate the earlier conjecture that in general the active (percolating) phases possess the hierarchical structure (tower of percolation patterns), where more complicated patterns emerge on the top of coexistent patterns of lesser complexity. Plethora of different patterns emerge via cascades of continuous transitions. We detect five phases with distinct patterns of percolation within the active phase of the model. All transitions on the phase diagram belong to the directed percolation universality class, as confirmed by the scaling analysis. To accommodate the case of multiple percolating phases the extension of the Janssen-Grassberger conjecture is proposed.