THE MANY FACES OF PERCOLATION

The theory of percolation deals with the appearance of large connected domains between randomly interlinked nodes and with the spreading of non-conserved ‘agents’ over these domains. Near threshold, when such domains just barely exist, they are typically sparse and fractal, making the transition from disconnectedness to connectedness a “second order” or continuous phase transition. We first review the salient features of this ‘ordinary’ percolation transition and the role it plays within the emergent ‘complexity science’. After that, we discuss alternative scenarios where connectedness can pop up more abruptly, leading to “first order” or discontinuous phase transitions – or even to ultrasmooth “infinite order” transitions. In particular, we show that cooperativity between spreading agents can have a large influence on the threshold behavior.