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We show, in general, that when a discontinuity of either zeroth-order or first-order takes place in an order parameter such as the chiral condensate, discontinuities of the same order emerge in other order parameters such as the Polyakov loop. A condition for the coexistence theorem to be valid is clarified. Consequently, only when the condition breaks down, zeroth-order and first-order discontinuities can coexist on a phase boundary. We show with the Polyakov-loop extended Nambu--Jona-Lasinio model that such a type of coexistence is realized in the imaginary chemical potential region of the QCD phase diagram. We also present examples of coexistence of the same-order discontinuities in the real chemical potential region.
The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, mu_B and mu_{iso}, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type ei
We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark
We present the phase diagram and the fluctuations of different conserved charges like quark number, charge and strangeness at vanishing chemical potential for the 2+1 flavor Polyakov Loop extended Nambu--Jona-Lasinio model with eight-quark interactio
We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $mu_5$, increases. The two crossove
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 c