Higher-order Ising model on hypergraphs

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,...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Robiglio, Thomas, Leonardo Di Gaetano, Altieri, Ada, Petri, Giovanni, Battiston, Federico
Format: Article
Language:English
Subjects:
Critical point
Dynamical systems
Ising model
Many body problem
Phase transitions
Online Access:Get full text
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Summary: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 na\"ive 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.
ISSN:2331-8422