  We study the onset of a classical order parameter after a second-order phase
transition in quantum field theory. We consider a quantum scalar field theory
in which the system-field (long-wavelength modes), interacts with its
environment, represented both by a set of scalar fields and by its own
short-wavelength modes. We compute the decoherence times for the system-field
modes and compare them with the other time scales of the model. We analyze
different couplings between the system and the environment for slow quenches.
Within our approximations decoherence is in general a short time event.
