  We study the dynamics of the Peccei-Quinn (PQ) phase transition for the QCD
axion. In weakly coupled models the transition is typically second order except
in the region of parameters where the PQ symmetry is broken through the
Coleman-Weinberg mechanism. In strongly coupled realizations the transition is
often first order. We show examples where the phase transition leads to strong
supercooling lowering the nucleation temperature and enhancing the stochastic
gravitational wave signals. The models predict a frequency peak in the range
100-1000 Hz with an amplitude that is already within the sensitivity of LIGO
and can be thoroughly tested with future gravitational wave interferometers.
