  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.
