Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911332161290240 |
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| author | Wu, Shuonan Xie, Yuchen Pan, Deng Zhang, Lei Jin, Yuliang |
| author_facet | Wu, Shuonan Xie, Yuchen Pan, Deng Zhang, Lei Jin, Yuliang |
| contents | According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture in three-dimensional systems remains challenging, where the energy barriers become finite. Here, we numerically explore the energy landscape of granular models near the jamming transition using a saddle dynamics algorithm to locate both local energy minima and saddles. The multi-scale distances and energy barriers between minima are characterized by two metrics, both of which exhibit signatures of an ultrametric space. The scale-free distribution of energy barriers reveals that the landscape is hierarchical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter Wu, Shuonan Xie, Yuchen Pan, Deng Zhang, Lei Jin, Yuliang Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture in three-dimensional systems remains challenging, where the energy barriers become finite. Here, we numerically explore the energy landscape of granular models near the jamming transition using a saddle dynamics algorithm to locate both local energy minima and saddles. The multi-scale distances and energy barriers between minima are characterized by two metrics, both of which exhibit signatures of an ultrametric space. The scale-free distribution of energy barriers reveals that the landscape is hierarchical. |
| title | Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2512.19229 |