  The order parameter for the pure Yang-Mills phase transition is the Polyakov
loop, which encodes the symmetries of the Z_N center of the SU(N) gauge group.
The physical degrees of freedom of any asymptotically free gauge theory are
hadronic states. Using the Yang-Mills trace anomaly and the exact Z_N symmetry
we show that the transfer of information from the order parameter to hadrons is
complete.
