Phase diagram in the imaginary chemical potential region and extended Z3   symmetry
  Phase transitions in the imaginary chemical potential region are studied by the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model that possesses the extended Z3 symmetry. The extended Z3 invariant quantities such as the partition function, the chiral condensate and the modifed Polyakov loop have the Roberge-Weiss (RW) periodicity. There appear four types of phase transitions; deconfinement, chiral, Polykov-loop RW and chiral RW transitions. The orders of the chiral and deconfinement transitions depend on the presence or absence of current quark mass, but those of the Polykov-loop RW and chiral RW transitions do not. The scalar-type eightquark interaction newly added in the model makes the chiral transition line shift to the vicinity of the deconfiment transition line. 
Yuji Sakai, Kouji Kashiwa, Hiroaki Kouno, Masanobu Yahiro