Suppression effect on the Berezinskii-Kosterlitz-Thouless transition in growing networks

The percolation transition in growing networks can be of infinite order, following the Berezinskii-Kosterlitz-Thouless (BKT) transition. Examples can be found in diverse systems, including coauthorship networks and protein interaction networks. Here, we investigate how such an infinite-order percolation transition is changed by the global suppression (GS) effect. We find that the BKT infinite-order transition breaks down, but the features of infinite-order, second-order, and first-order transitions all emerge in a single framework. Owing to the GS effect, the transition point p(c) is delayed, below which the critical region is extended. The power-law behavior of the cluster size distribution reaches the state with the exponent tau = 2 at p(c,) suggesting that the system has the maximum diversity of cluster sizes and a first-order percolation transition occurs at p(c).