Higher-order Ising model on hypergraphs
Thomas Robiglio1,2, Leonardo Di Gaetano2, Ada Altieri3
1Interdisciplinary Transformation University Austria, Inverse Complexity Lab, IT:U , 4040 Linz, Austria.
None:
Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here, we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the ordered and the disordered phase. By a mean-field treatment, we show that the transition is continuous when only three-body interactions are considered, but becomes abrupt when interactions of higher orders are introduced. Using a Georges-Yedidia expansion to go beyond a naïve mean-field approximation, we reveal a quantitative shift in the critical point of the phase transition, which does not affect the universality class of the model. Finally, we compare our results with traditional p-spin models with many-body interactions. Our work unveils new collective phenomena on complex interacting systems, revealing the importance of investigating higher-order systems beyond three-body interactions.
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