  Facilitated spin models were introduced some decades ago to mimic systems
characterized by a glass transition. Recent developments have shown that a
class of facilitated spin models is also able to reproduce characteristic
signatures of the structural relaxation properties of glass-forming liquids.
While the equilibrium phase diagram of these models can be calculated
analytically, the dynamics are usually investigated numerically. Here we
propose a new network-based approach, called approximate master equation (AME),
to the dynamics of the Fredrickson-Andersen model. The approach correctly
predicts the critical temperature at which the glass transition occurs. We also
find excellent agreement between the theory and the numerical simulations for
the transient regime, except in close proximity of the liquid-glass transition.
Finally, we analytically characterize the critical clusters of the model and
show that the departures between our AME approach and the Monte Carlo can be
related to the large interface between frozen and unfrozen spins at
temperatures close to the glass transition.
