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Abstract <p>A model of a one-dimensional directed percolation process is investigated using Monte Carlo and dimensional scaling methods. The results obtained confirm the earlier hypothesis that in general active (percolating) phases feature a hierarchical structure, where more complex patterns appear on top of coexisting simple ones. Five phases with different percolation patterns have been found in the active phase of the model. A detailed scaling analysis of the dipole phase manifested within the active phase of directional percolation is presented.</p>

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Hidden Patterns in One-Dimensional Directed Percolation Process

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • P. A. Ovchinnikov,
  • K. S. Soldatov,
  • V. Yu. Kapitan,
  • G. Yu. Chitov

摘要

Abstract

A model of a one-dimensional directed percolation process is investigated using Monte Carlo and dimensional scaling methods. The results obtained confirm the earlier hypothesis that in general active (percolating) phases feature a hierarchical structure, where more complex patterns appear on top of coexisting simple ones. Five phases with different percolation patterns have been found in the active phase of the model. A detailed scaling analysis of the dipole phase manifested within the active phase of directional percolation is presented.