Color symmetry and ferromagnetism in Potts spin glass

We consider the Potts spin glass with additional ferromagnetic interaction parametrized by $t$. It has long been observed that the Potts color symmetry breaking for the spin glass order parameter is closely related to the ferromagnetic phase transition. To clarify this, we identify a single critical value $t_{\mathrm{c}}$, which marks the onset of both color symmetry breaking and the transition to ferromagnetism.