Higher-order Ising model on hypergraphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915040238501888 |
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| 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 |