Anomalous percolation transitions beyond the BKT transition in growing networks

Abstract

Since the discovery a half century ago that 1/r^2-type long-range interactions in the one-dimensional Ising model change the phase transition type, long-range interactions in diverse systems have received considerable attention. Recently, this interest extended to global suppression dynamics in the percolation transition, which changes a second-order transition to first order. Here, we investigate how the Berezinskii-Kosterlitz-Thouless (BKT) transition is changed by the global suppression effect. In fact, this effect often arises in real-world complex systems, yet it is not appropriately accounted for in models. We find that the BKT transition breaks down, but the features of infinite-, second-, and first-order transitions all emerge as the link occupation probability is controlled. Moreover, we find that such growing networks exhibit maximum diversity, causing the mean cluster size to diverge without formation of a giant cluster. We elucidate the underlying mechanisms and show that such anomalous transitions are universal.