Higher-order Ising model on hypergraphs

Fuente: arXiv
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Main Authors: Robiglio, Thomas, Di Gaetano, Leonardo, Altieri, Ada, Petri, Giovanni, Battiston, Federico
Format: Preprint
Published: 2024
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_version_ 1866915040238501888
author Robiglio, Thomas
Di Gaetano, Leonardo
Altieri, Ada
Petri, Giovanni
Battiston, Federico
author_facet Robiglio, Thomas
Di Gaetano, Leonardo
Altieri, Ada
Petri, Giovanni
Battiston, Federico
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19618
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Higher-order Ising model on hypergraphs
Robiglio, Thomas
Di Gaetano, Leonardo
Altieri, Ada
Petri, Giovanni
Battiston, Federico
Statistical Mechanics
Physics and Society
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.
title Higher-order Ising model on hypergraphs
topic Statistical Mechanics
Physics and Society
url https://arxiv.org/abs/2411.19618