Narrow Results

In this paper, we use a separable gluon propagator model to study the Quantum Chromodynamics (QCD) phase transition at finite temperature and chiral chemical potential. Using this model, we calculate the quark condensate and the chiral susceptibility at finite temperature and chiral chemical potential both in the chiral limit and at finite current quark mass. Based on these, we obtain the QCD phase diagram in the μ₅-T plane.

We have gone through a comparative study on two different kinds of bulk viscosity expressions by using a common dynamical model. The Polyakov–Nambu–Jona-Lasinio (PNJL) model in the realm of mean-field approximation, including up to eight quark interactions for 2+1 flavor quark matter, is treated for this common dynamics. We have probed the numerical equivalence as well as discrepancy of two different expressions for bulk viscosity at vanishing quark chemical potential. Our estimation of bulk viscosity to entropy density ratio follows a decreasing trend with temperature, which is observed in most of the earlier investigations. We have also extended our estimation for finite values of quark chemical potential.

The thermodynamic behavior of the two-flavor (N_f = 2) three-color (N_c = 3) Polyakov-loop-extended Nambu–Jona-Lasinio (PNJL) model at the finite chemical potential is investigated. New lattice gluon data for gluon thermodynamics are used defining the effective potential within polynomial and logarithmic forms of its approximation. We study the effects of using different sets of data and different forms of the potential on thermodynamic properties of hot and dense matter. It is found that the PNJL thermodynamics depends stronger on the form of the effective potential than on the used lattice data set. Particular attention is paid to the phase diagram in the (T, μ) plane.

An attempt is made to resolve certain incongruities within the Nambu–Jona-Lasinio (NJL) and Polyakov loop extended NJL models (PNJL) which currently are used to extract the thermodynamic characteristics of the quark–gluon system. It is argued that the most attractive resolution of these incongruities is the possibility to obtain the thermodynamic potential directly from the corresponding extremum conditions (gap equations) by integrating them, an integration constant being fixed in accordance with the Stefan–Boltzmann law. The advantage of the approach is that the regulator is kept finite both in divergent and finite valued integrals at finite temperature and chemical potential. The Pauli–Villars regularization is used, although a standard 3D sharp cutoff can be applied as well.

The two-flavor Polyakov-loop extended model is generalized by taking into account the effective four-quark vector-type interaction with the coupling strengths, which are endowed with a dependence on the Polyakov field Φ. The effective vertex generates entanglement interaction between the Polyakov loop and the chiral condensate. We investigate the influence of an additional quark vector interaction and the entanglement interaction on thermodynamics of a quark system and in particular on the location of the critical end-point at the given chemical potential or quark density. It is shown that the finite value of the singlet vector interaction strength G_v improves the model agreement with the lattice data. The influence of the nonzero G_v and entanglement on the thermodynamic observables and the curvature of the crossover boundary in the T – μ plane is also examined.

To investigate the finite-volume effects on the chiral symmetry restoration and the deconfinement transition for a quantum chromodynamics (QCD) system with $N_f=2$ (two quark flavors), we apply the Polyakov-loop extended Nambu–Jona-Lasinio model by introducing a chiral chemical potential ${\mu }_5$ artificially. The final numerical results indicate that the introduced chiral chemical potential does not change the critical exponents, but shifts the location of critical end point (CEP) significantly; the ratios for the chiral chemical potentials and temperatures at CEP, ${\mu }_c/{\mu }_{5c}$ and $T_c/T_{5c}$, are significantly affected by the system size $R$. The behavior is that $T_c$ increases slowly with ${\mu }_5$ when $R$ is “large” and $T_c$ decreases first and then increases with ${\mu }_5$ when $R$ is “small.” It is also found that for a fixed ${\mu }_5$, there is a $R_{\mathrm{\text{min}}}$, where the critical end point vanishes and the whole phase diagram becomes a crossover when $R<R_{\mathrm{\text{min}}}$. Therefore, we suggest that for the heavy-ion collision experiments, which is to study the possible location of CEP, the finite-volume behavior should be taken into account.