Jamming as a topological satisfiability transition with contact number hyperuniformity and criticality
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915352370216960 |
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| author | Shang, Jin Wang, Yinqiao Pan, Deng Jin, Yuliang Zhang, Jie |
| author_facet | Shang, Jin Wang, Yinqiao Pan, Deng Jin, Yuliang Zhang, Jie |
| contents | The jamming transition between flow and amorphous-solid states exhibits paradoxical properties characterized by hyperuniformity (suppressed spatial fluctuations) and criticality (hyperfluctuations), whose origin remains unclear. Here we model the jamming transition by a topological satisfiability transition in a minimum network model with simultaneously hyperuniform distributions of contacts, diverging length scales and scale-free clusters. We show that these phenomena stem from isostaticity and mechanical stability: the former imposes a global equality, and the latter local inequalities on arbitrary sub-systems. This dual constraint bounds contact number fluctuations from both above and below, limiting them to scale with the surface area. The hyperuniform and critical exponents of the network model align with those of frictionless jamming, suggesting a new universality class of non-equilibrium phase transitions. Our results provide a minimal, dynamics-independent framework for jamming criticality and hyperuniformity in disordered systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_16474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jamming as a topological satisfiability transition with contact number hyperuniformity and criticality Shang, Jin Wang, Yinqiao Pan, Deng Jin, Yuliang Zhang, Jie Soft Condensed Matter The jamming transition between flow and amorphous-solid states exhibits paradoxical properties characterized by hyperuniformity (suppressed spatial fluctuations) and criticality (hyperfluctuations), whose origin remains unclear. Here we model the jamming transition by a topological satisfiability transition in a minimum network model with simultaneously hyperuniform distributions of contacts, diverging length scales and scale-free clusters. We show that these phenomena stem from isostaticity and mechanical stability: the former imposes a global equality, and the latter local inequalities on arbitrary sub-systems. This dual constraint bounds contact number fluctuations from both above and below, limiting them to scale with the surface area. The hyperuniform and critical exponents of the network model align with those of frictionless jamming, suggesting a new universality class of non-equilibrium phase transitions. Our results provide a minimal, dynamics-independent framework for jamming criticality and hyperuniformity in disordered systems. |
| title | Jamming as a topological satisfiability transition with contact number hyperuniformity and criticality |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2506.16474 |