Competing heterogeneities shape ordering via higher-order interactions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918531277258752 |
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| author | Son, Gangmin Battiston, Federico Lee, Deok-Sun Goh, K. -I. |
| author_facet | Son, Gangmin Battiston, Federico Lee, Deok-Sun Goh, K. -I. |
| contents | Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double transitions can arise, where the symmetry-breaking continuous transition is driven by pairs or by hubs, respectively. When both heterogeneities coexist, cross-order degree correlations further modulate the phase diagram, with anticorrelation delaying the group-driven discontinuous jump and broadening the hysteretic region. Our results reveal the intricate interplay between size and degree heterogeneities in collective phenomena beyond pairwise interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30948 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Competing heterogeneities shape ordering via higher-order interactions Son, Gangmin Battiston, Federico Lee, Deok-Sun Goh, K. -I. Statistical Mechanics Physics and Society Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double transitions can arise, where the symmetry-breaking continuous transition is driven by pairs or by hubs, respectively. When both heterogeneities coexist, cross-order degree correlations further modulate the phase diagram, with anticorrelation delaying the group-driven discontinuous jump and broadening the hysteretic region. Our results reveal the intricate interplay between size and degree heterogeneities in collective phenomena beyond pairwise interactions. |
| title | Competing heterogeneities shape ordering via higher-order interactions |
| topic | Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2605.30948 |