Higher-order Ising model on hypergraphs
Abstract
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 -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.
Cite
@article{arxiv.2411.19618,
title = {Higher-order Ising model on hypergraphs},
author = {Thomas Robiglio and Leonardo Di Gaetano and Ada Altieri and Giovanni Petri and Federico Battiston},
journal= {arXiv preprint arXiv:2411.19618},
year = {2024}
}