Emergence of classicality in quantum phase transitions

We show that the long wavelength modes of a field become classical during a second order phase transition because of the interaction with the short wavelength modes of the field. In a massive scalar field model the number and thermal states of long wavelength modes, whose Wigner functions are sharply peaked around the classical trajectories during the phase transition, exhibit only classical correlation without achieving quantum decoherence. In a linearly coupled scalar field model, the long wavelength modes are shown to effectively achieve quantum decoherence because of the mode mixing. Finally we define a quantal ordering parameter that is linear in the field variable and satisfies the classical field equation