  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.
On the other side 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 construct a model able to communicate to the hadrons the
information carried by the order parameter.
