Abstract
The dynamical behaviours of a kinetically constrained spin model (Fredrickson–Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is observed that the time-dependent solutions of the derived dynamical systems obtained by the perturbation analysis become systematically closer to the results obtained by Monte Carlo simulations as the order of the perturbation series is increased. This systematic perturbation analysis also clarifies the existence of a dynamical scaling law, which provides an implication for a universal relation between a size scale and a timescale near the nonergodic transition.
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