Synergistic Signatures of Group Mechanisms in Higher-Order Systems

The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order mechanisms and higher-order behavioral observables in two representative models with group interactions: a simplicial Ising model and a social contagion model. In both systems, we find that group (higher-order) interactions show emergent synergistic (higher-order) behavior. The emergent synergy appears only at the group level and depends in a complex, nonlinear way on the trade-off between the strengths of the low- and higher-order mechanisms and is invisible to low-order behavioral observables. Our work sets the basis for systematically investigating the relation between causal mechanisms and behavioral patterns in complex networked systems with group interactions, offering a robust methodological framework to tackle this challenging task.