  We consider C*-algebras of finite higher-rank graphs along with their
rotational action. We show how the entropy theory of product systems with
finite frames applies to identify the phase transitions of the dynamics. We
compute the positive inverse temperatures where symmetry breaks, and in
particular we identify the subharmonic parts of the gauge-invariant equilibrium
states. Our analysis applies to positively weighted rotational actions through
a recalibration of the entropies.
