2024/09/25 by P. A. Ovchinnikov, Konstantin Soldatov, Ovchinnikov, P. +5 · 2 citations
Mathematics · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2409.16786
openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.