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

TL;DR

This paper analytically solves the critical dynamics of the Kob-Andersen model on Bethe lattices, revealing that its behavior aligns with Mode-Coupling Theory and validating predictions through numerical simulations.

Contribution

It provides the first analytical solution for the critical dynamics of the Kob-Andersen model on Bethe lattices, connecting it to Mode-Coupling Theory.

Findings

Critical behavior follows Mode-Coupling Theory equations

Predicted dynamical exponents match numerical simulations

Applicable to both continuous and discontinuous transitions

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.