  We analyze the quantum to classical transition of the order parameter in
second order phase transitions. We consider several toy models in non
relativistic quantum mechanics. We study the dynamical evolution of a wave
packet initially peaked around a local maximum of the potential using
variational approximations and also exact numerical results. The influence of
the environment on the evolution of the density matrix and the Wigner function
is analyzed in great detail. We also discuss the relevance of our results to
the analysis of phase transitions in field theory. In particular, we argue that
previous results about classicality of the order parameter in O(N) models may
be consequences of the large $N$ approximation.
