Anomalous percolation transitions beyond the BKT transition in growing networks

TL;DR

This paper explores how global suppression effects alter the Berezinskii-Kosterlitz-Thouless transition in growing networks, revealing a range of anomalous percolation behaviors including divergence of mean cluster size without giant cluster formation.

Contribution

It demonstrates that global suppression effects fundamentally change the BKT transition, leading to diverse and universal anomalous percolation phenomena in growing networks.

Findings

BKT transition breaks down under global suppression.

Mean cluster size diverges without forming a giant cluster.

Multiple types of phase transitions emerge depending on link probability.

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.