Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model

Gianmarco Perrupato; Tommaso Rizzo

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arXiv · 2505.16451

Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model

Gianmarco Perrupato·Tommaso Rizzo

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Abstract

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.

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Gianmarco Perrupato, Tommaso Rizzo. 2025-05-22. Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model. https://arxiv.org/abs/2505.16451

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