Universal Microscopic Mechanism of Hybrid Percolation Transitions

Explore the universal microscopic mechanism of hybrid percolation transitions (HPTs) in this comprehensive lecture. Delve into the two ways dynamic transitions can occur: cluster pruning with suppression of loop formation of cut links and cluster merging with suppression of large cluster creation. Uncover the detailed microscopic framework for cluster merging models, revealing the three-step process behind HPT features. Learn about the accumulation of medium-sized clusters, rapid growth of giant clusters through merging, and the transition to Erdős-Rényi type dynamics. Examine the critical behavior characterized by two sets of exponents related to order parameter and cluster size distribution, connected through a scaling relation. Gain insights into extensive numerical simulations and specific finite-size scaling analysis methods used to handle large fluctuations at the transition point. Discover a unified theoretical framework for understanding hybrid percolation transitions across different models.