  The propagation of information in social, biological and technological
systems represents a crucial component in their dynamic behavior. When limited
to pairwise interactions, a rather firm grip is available on the relevant
parameters and critical transitions of these spreading processes, most notably
the pandemic transition, which indicates the conditions for the spread to cover
a large fraction of the network. The challenge is that, in many relevant
applications, the spread is driven by higher order relationships, in which
several components undergo a group interaction. To address this, we analyze the
spreading dynamics in a simplicial complex environment, designed to capture the
coexistence of interactions of different orders. We find that, while pairwise
interactions play a key role in the initial stages of the spread, once it gains
coverage, higher order simplices take over and drive the contagion dynamics.
The result is a distinctive spreading phase diagram, exhibiting a discontinuous
pandemic transition, and hence offering a qualitative departure from the
traditional network spreading dynamics.
