Higher-order Ising model on hypergraphs

TL;DR

This paper introduces a higher-order Ising model on hypergraphs, analyzing its phase transitions and revealing new collective phenomena due to interactions beyond three-body terms.

Contribution

It presents a novel higher-order Ising model, characterizes its phase transitions, and compares it with traditional p-spin models, advancing understanding of complex interactions.

Findings

Transition is continuous with three-body interactions.

Transition becomes abrupt with higher-order interactions.

Critical point shifts without changing universality class.

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 $p$-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.