Global suppression effect on the infinite-order percolation transitions in growing networks

The percolation transition in growing networks can be of infinite order, following the Berezinskii-Kosteritz-Thouless (BKT) transition. Examples can be found in diverse systems ranging from socio- to bio-networks such as the coauthorship networks and the protein interaction networks. Here we are interested in how such an infinite-order percolation transition is changed by global suppression (GS) effect. In fact, about a half century ago, Thouless showed that 1/r²-type long-range interactions in the one-dimensional Ising model change the phase transition type from second order to first order. One may think that the GS dynamics plays a similar role of changing percolation transitions in complex systems. We show that the BKT transition breaks down, but the features of infinite-order, second-order, and first-order transitions all emerge in a single framework. The critical region below the BKT transition point is extended and the power-law behavior of the cluster size distribution reaches the state with the exponent two, suggesting that the system has the maximum diversity of cluster sizes. We also elucidate the underlying mechanisms and show that those features are universal. Forming such extereme diversity by the GS dynamics may be helpful for establishing stablized complex systems.