Phase Structure of Nambu-Jona-Lasinio Model at Finite Isospin Density
  In the frame of flavor SU(2) Nambu--Jona-Lasinio model with $U_A(1)$ breaking term we found that, the structure of two chiral phase transition lines does not exist at low isospin density in real world, and the critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum. 
Lianyi He and Pengfei Zhuang