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arXiv · 2512.19229

Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter

Shuonan Wu·Yuchen Xie·Deng Pan·Lei Zhang·Yuliang Jin
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Abstract

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.

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Shuonan Wu, Yuchen Xie, Deng Pan, Lei Zhang, Yuliang Jin. 2025-12-22. Hierarchical and ultrametric barriers in the energy landscape of jammed granular matter. https://arxiv.org/abs/2512.19229

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