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A hybrid percolation transition (HPT) exhibits both discontinuity of theorder parameter and critical behavior at the transition point. Such dynamictransitions can occur in two ways: by cluster pruning with suppression of loopformation of cut links or by cluster merging with suppression of the creationof large clusters. While the microscopic mechanism of the former is understoodin detail, a similar framework is missing for the latter. By studying twodistinct cluster merging models, we uncover the universal mechanism of thefeatures of HPT-s at a microscopic level. We find that these features occur inthree steps: (i) medium-sized clusters accumulate due to the suppression rulehindering the growth of large clusters, (ii) those medium size clusterseventually merge and a giant cluster increases rapidly, and (iii) thesuppression effect becomes obsolete and the kinetics is governed by theErd\H{o}s-R\'enyi type of dynamics. We show that during the second and thirdperiod, the growth of the largest component must proceed in the form of aDevil's staircase. We characterize the critical behavior by two sets ofexponents associated with the order parameter and cluster size distribution,which are related to each other by a scaling relation. Extensive numericalsimulations are carried out to support the theory where a specific method isapplied for finite-size scaling analysis to enable handling the largefluctuations of the transition point. Our results provide a unified theoreticalframework for the HPT.

Unified framework for hybrid percolation transitions based on microscopic dynamics