Systematic perturbation approach for a dynamical scaling law in a kinetically constrainedspin model

Abstract

The dynamical behaviours of a kinetically constrained spin model (Fredrickson–Andersenmodel) on a Bethe lattice are investigated by a perturbation analysis that provides exactfinal states above the nonergodic transition point. It is observed that the time-dependentsolutions of the derived dynamical systems obtained by the perturbation analysis becomesystematically closer to the results obtained by Monte Carlo simulations as the order ofthe perturbation series is increased. This systematic perturbation analysis alsoclarifies the existence of a dynamical scaling law, which provides an implication fora universal relation between a size scale and a timescale near the nonergodictransition.