标题： 平均场Kob-Andersen模型的临界动力学的解 显示英文标题

标题： The Solution of the Critical Dynamics of the Mean-Field Kob-Andersen Model

摘要： 我们解析地解决了在Bethe格点上超冷液体的Kob-Andersen动力学受限模型的临界动力学，采用了基于腔方法的组合论证。 对于任意的图连通性z和促进参数m，我们证明序参量的临界行为受控于与模式耦合理论中发现的运动方程等价的方程。 通过与包括连续和不连续转变场景的数值模拟直接比较，验证了关于动态指数的结果预测。 显示英文摘要

摘要： 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.