Unified framework for hybrid percolation transitions based on microscopic dynamics

We study a hybrid percolation transition (HPT), which exhibits both a discontinuity of the order parameter and critical behavior at the transition point. HPT can be driven by either local or nonlocal information. While the critical branching mechanism is well understood for the local process, a comparable framework is lacking for nonlocal processes. Here, we uncover a universal mechanism for HPT with nonlocal suppression and provide a microscopic system picture before the transition point. The critical behavior in the supercritical regime is characterized by two sets of critical exponents associated with the order parameter and cluster size distribution. These critical exponents are linked to novel critical aging dynamics observed in the subcritical regime. The results contribute to a comprehensive understanding of HPTs in both local and nonlocal processes, completing a unified framework for such transitions.