The mixed quark-gluon condensate is another chiral order parameter in QCD, which plays an important role in the application of QCD sum rules. In this letter, we study the properties of quark-gluon mixed condensate at finite temperature and quark chemical potential in the framework of global color symmetry model. Using an infrareddominant model gluon two-point function, we find that the behavior of quark-gluon mixed condensate at finite temperature and chemical potential is similar to that of the quark condensate, and both of them give the same information about chiral phase transition. We also find that the ratio of these two condensates is insensitive to the temperature and chemical potential, which supports the conclusion obtained recently by the authors using quenched lattice QCD ( They only studied the nature of the mixed quark-gluon condensate at finite temperature ).

The dual observables as order parameters for center symmetry are tested at finite isospin chemical potential $\mu_I$ in a Polyakov-loop enhanced chiral model of QCD with physical quark masses. As a counterpart of the dressed Polyakov-loop, the first Fourier moment of pion condensate is introduced for $\mu_I>{m_\pi}/{2}$ under the temporal twisted boundary conditions for quarks. We demonstrate that this dual condensate exhibits the similar temperature dependence as the conventional Polyakov-loop. We confirm that its rapid increase with $T$ is driven by the evaporating of pion condensation. On the other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which even decreases with $T$ at low temperatures due to the influence of pion condensate. We thus argue that in QCD the critical temperature extracting from a dual observable may have nothing to do with the quark confinement-deconfinement transition if the quark mass is very small.Comment: 8 pages, 6 figure

The flavor-mixing induced by the mismatched vector-isoscalar and vector-isovector interactions at finite baryon chemical potential µ and isospin chemical potential µI is demonstrated in the Nambu-Jona-Lasinio (NJL) type model of QCD. The influence of this non-anomaly flavor-mixing on the possible separate chiral transitions at nonzero µI is studied under the assumption of the effective restoration of the U (1)A symmetry. We find that for the weak isospin asymmetry, the two separate phase boundaries found previously can be converted into one only if the vector-isovector coupling g v v is significantly stronger than the vector-isoscalar one g s v without the axial anomaly. When the weak Kabayashi-Maskawa-'t Hooft (KMT) interaction is included, we find that the separation of the chiral transition with two critical endpoints for the relatively strong isospin asymmetry can still be removed owning to the vector interactions. In this case, it is not the vector coupling difference but the strength of g v v which is crucial for the only phase boundary. We also point out that, in the NJL-type model with mismatched vector interactions, the recently proposed equivalence for chiral transitions at finite µ and µI does not hold even at the mean field approximation.

The recent lattice calculation at finite axial chemical potential suggests that the induced current density of the chiral magnetic effect (CME) is somehow suppressed compared with the standard analytical formula. We show in a Nambu-Jona-Lasino-type model of QCD that such a suppression is a natural result when considering the influence of the attractive axial-vector interaction. We point out that the lattice result does not need to be quantitatively consistent with the analytical formula due to the chirality densitydensity correlation. We also investigate the nonperturbative effect of instanton molecules on the CME. Since an unconventional repulsive axial-vector interaction is induced, the CME will be enhanced significantly by the instanton-anti-instanton pairings. Such a prediction needs to be tested by more improved lattice simulations. We further demonstrate that the axial-vector interaction plays an important role on the T À A phase diagram. 1 The magnetic field strength can be translated into the CGS system with the identity m 2 % 10 18 Gauss, where m ¼ 140 MeV.

No abstract