  Complex networks have been successfully used to describe the spread of
diseases in populations of interacting individuals. Conversely, pairwise
interactions are often not enough to characterize social contagion processes
such as opinion formation or the adoption of novelties, where complex
mechanisms of influence and reinforcement are at work. Here we introduce a
higher-order model of social contagion in which a social system is represented
by a simplicial complex and contagion can occur through interactions in groups
of different sizes. Numerical simulations of the model on both empirical and
synthetic simplicial complexes highlight the emergence of novel phenomena such
as a discontinuous transition induced by higher-order interactions. We show
analytically that the transition is discontinuous and that a bistable region
appears where healthy and endemic states co-exist. Our results help explain why
critical masses are required to initiate social changes and contribute to the
understanding of higher-order interactions in complex systems.
