Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914074323845120 |
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| author | Perrupato, Gianmarco Rizzo, Tommaso |
| author_facet | Perrupato, Gianmarco Rizzo, Tommaso |
| contents | We analytically solve the critical dynamics of the Kob-Andersen kinetically constrained model of supercooled liquids on the Bethe lattice, employing a combinatorial argument based on the cavity method. For arbitrary values of graph connectivity z and facilitation parameter m, we demonstrate that the critical behavior of the order parameter is governed by equations of motion equivalent to those found in Mode-Coupling Theory. The resulting predictions for the dynamical exponents are validated through direct comparisons with numerical simulations that include both continuous and discontinuous transition scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model Perrupato, Gianmarco Rizzo, Tommaso Disordered Systems and Neural Networks Statistical Mechanics We analytically solve the critical dynamics of the Kob-Andersen kinetically constrained model of supercooled liquids on the Bethe lattice, employing a combinatorial argument based on the cavity method. For arbitrary values of graph connectivity z and facilitation parameter m, we demonstrate that the critical behavior of the order parameter is governed by equations of motion equivalent to those found in Mode-Coupling Theory. The resulting predictions for the dynamical exponents are validated through direct comparisons with numerical simulations that include both continuous and discontinuous transition scenarios. |
| title | Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2505.16451 |