Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model

The Polyakov-loop-extended Nambu Jona-Lasinio model is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,\mu_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and the phase transition for isospin symmetry restoration perfectly coincide with the crossover phase transition for Polyakov loop. These results is agreement with the Lattice QCD data