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Inverting the Achlioptas rule for explosive percolation.

R A da Costa1, S N Dorogovtsev1,2, A V Goltsev1,2

  • 1Departamento de Física da Universidade de Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.

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This summary is machine-generated.

This study reverses Achlioptas processes, merging largest clusters instead of smallest. This "reverse percolation" shows a continuous transition similar to ordinary percolation but in less connected systems.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Achlioptas processes typically merge small clusters, leading to explosive percolation.
  • This results in a delayed giant cluster formation and anomalous transition features.

Purpose of the Study:

  • To investigate a reverse Achlioptas process where largest clusters merge.
  • To theoretically analyze this reverse percolation and its scaling properties.

Main Methods:

  • Developed a theoretical framework using the Smoluchowsky equation.
  • Analyzed the percolation threshold and critical phenomena.

Main Results:

  • Identified a continuous percolation transition in the reverse process.
  • Characterized critical exponents, amplitudes, and scaling functions.
  • Found qualitative similarity to ordinary percolation despite lower connectivity.

Conclusions:

  • The reverse cluster merging process exhibits a continuous transition.
  • This transition shares similarities with ordinary percolation but occurs in less connected systems.