  We consider the critical short-time evolution of magnetic and
droplet-percolation order parameters for the Ising model in two and three
dimensions, through Monte-Carlo simulations with the (local) heat-bath method.
We find qualitatively different dynamic behaviors for the two types of order
parameters. More precisely, we find that the percolation order parameter does
not have a power-law behavior as encountered for the magnetization, but
develops a scale (related to the relaxation time to equilibrium) in the
Monte-Carlo time. We argue that this difference is due to the difficulty in
forming large clusters at the early stages of the evolution. Our results show
that, although the descriptions in terms of magnetic and percolation order
parameters may be equivalent in the equilibrium regime, greater care must be
taken to interprete percolation observables at short times. In particular, this
concerns the attempts to describe the dynamics of the deconfinement phase
transition in QCD using cluster observables.
