Synergistic effects of spatial connections in shaping social contagions on higher-order lattice networks

Extensive studies revealed that the spatial networks exhibits low-order (pairwise interaction) and higher-order interaction (multiple interaction), which markedly affect the spreading dynamics. However, theoretical studies about the synergistic effects of the two interactions shaping social contagions (e.g., behavior spreading) are still lacking. To this end, we propose a social contagion model to describe the behavior dynamics on higher-order lattice networks. Through extensive simulations and the finite-size scaling method, the giant connected cluster of the global behavior adoption exhibits discontinuous and continuous phase transitions, which depend on the spatial network structures. Specifically, the system exhibits a discontinuous (continuous) phase transition when there are many long-range (short-range) hyperedges. We further calculate the relative contribution ratio of low-order and high-order contagions contributed by the two types of interactions, and reveal four distinct regions: Region I and Region IV exhibit absolute dominance of higher-order and low-order spread, respectively; Region II displays relative dominance of higher-order spread, while Region III shows relative dominance of low-order spread. A reduction in the low-order contagion threshold decreases the critical mass for the global behavior adoption, enhances the relative contributions of low-order contagion, and leads to an expansion of Region IV and a contraction of Region I.