Diverse types of percolation transitions

Abstract

Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently, however, many abrupt percolation transitions have been observed in complex systems. To illustrate such phenomena, considerable effort has been made to introduce models and construct theoretical frameworks for explosive, discontinuous, and hybrid percolation transitions. Experimental results have also been reported. In this review article, we describe such percolation models, their critical behaviors and universal features, and real-world phenomena.

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• Critical behavior of a two-step contagion model with multiple seeds
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Unified framework for hybrid percolation transitions based on microscopic dynamics
• Colored Percolation
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• Double Transition in a Model of Oscillating Percolation
• Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks
• Discontinuous emergence of a giant cluster in assortative scale-free networks