Ladder-QCD at finite isospin chemical potential

We use an effective QCD model (ladder-QCD) to explore the phase diagram for chiral symmetry breaking and restoration at finite temperature with different $u,d$ quark chemical potentials. In agreement with a recent investigation based on the Nambu-Jona-Lasinio model, we find that a finite pion condensate shows up for high enough isospin chemical potential $\mu_{I}=(\mu_{u}-\mu_{d})/2$. For small $\mu_{I}$ the phase diagram in the $(\mu_B,T)$ plane shows two first order transition lines and two critical ending points.