Thermodynamical properties of asymmetric strange quark matter using the Polyakov Chiral $\text{SU(3)}$ quark mean field (PCQMF) model at finite temperature and chemical potential have been investigated. Within the PCQMF model, the properties of quark matter are calculated through the scalar fields $σ$, $ζ$, $δ$ and $χ$, the vector fields $ω$, $ρ$ and $ϕ$ and the Polyakov loop fields $Φ$ and $\barΦ$. The isospin splitting of constituent quark masses is observed at large isospin asymmetry. The effect of temperature and strangeness fraction on energy per baryon and equation of state is found to be appreciable in quark matter. The effect of the Polyakov loop dynamics on several thermodynamical bulk quantities such as energy density, entropy density, and trace anomaly is presented and compared with recent lattice QCD results.
We consider how does the introduction of a Polyakov loop affects the spatially inhomogeneous quark condensate. The primary result of our work is that the existence of the spatially non-uniform chiral phase is confirmed within the Polyakov NJL model in a chiral limit. These findings are obtained both in a 3d-cutoff and in a Schwinger (proper time) regularization schemes.
We address a possible relation between the expectation value of the Polyakov loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models where constituent quarks and the Polyakov loop are coupled in a minimal way. To this end we use a center symmetry breaking Gaussian model for the Polyakov loop distribution which accurately reproduces gluodynamics data above the phase transition in terms of dimension 2 gluon condensate. The role played by the quantum and local nature of the Polyakov loop is emphasized.
The Nambu Jona-Lasinio model with a Polyakov loop 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 $(T,μ_I)$ 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 …
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature. For that purpose we analyse an effective model proposed by Gocksch and Ogilvie, which is constructed by the double expansion of strong coupling and large dimensionality. We make improvements in dealing with the model and then obtain plausible results for the behaviours of both the Polyakov loop and the chiral scalar condensate. The pseudo-critical temperature read from the Polyakov loop turns out to coincide exactly with that read from the chiral scalar condensate. Within the model study bas…
We use the Polyakov loop coupled quark-meson model to approximate low energy QCD and present results for the chiral and deconfinement transitions in the presence of a constant magnetic background $B$ at finite temperature $T$ and baryon chemical potential $μ_B$. We investigate effects of various gluoni potentials on the deconfinement transition with and without a fermionic backreaction at finite $B$. Additionally we investigate the effect of the Polyakov loop on the chiral phase transition, finding that magnetic catalysis at low $μ_B$ is present, but weakened by the Polyakov loop.
We discuss how the simultaneous crossovers of deconfinement and chiral restoration can be realized. We propose a dynamical mechanism assuming that the effective potential gives a finite value of the chiral condensate if the Polyakov loop vanishes. Using a simple model, we demonstrate that our idea works well for small quark mass, though there should be further constraints to reach the perfect locking of two phenomena.
We analyze the role played by the Polyakov loop in the description of the chiral phase transition within the framework of nonlocal SU(3) chiral models with flavor mixing. We show that its presence provides a substantial enhancement of the predicted critical temperature, bringing it to a better agreement with the most recent results of lattice calculations.
Heat kernel expansions at finite temperature of massless QCD and chiral quark models generate effective actions relevant for both low and high temperature QCD. The key relevance of the Polyakov Loop to maintain the large and non-perturbative gauge invariance at finite temperature is stressed.
We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result an…
We calculate the transport coefficients, drag and momentum diffusion, of a heavy quark in a thermalized plasma of light quarks in the background of Polyakov loop. Quark thermal mass and the gluon Debye mass are calculated in a non-trivial Polyakov loop background. The constituent quark masses and the Polyakov loop is estimated within a Polyakov loop quark meson (PQM) model. The relevant scattering amplitudes for heavy quark and light partons in the background of Polyakov loop has been estimated within the matrix model. We have also compared the results with the Polyakov loop parameter estimate…
We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponent…
We describe results for the confinement-deconfinement phase transition as predicted by the Nambu--Jona-Lasinio model where the local and quantum Polyakov loop is coupled to the constituent quarks in a minimal way (PNJL). We observe that the leading correlation of two Polyakov loops describes the chiral transition accurately. The effects of the current quark mass on the transition are also analysed.
The phase diagram at finite temperature and chemical potential for the Polyakov-NJL model with eight quark interactions is reviewed for the SU(3) flavor case.
The behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0$ MeV the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electr…
At finite temperature, chiral quark models do not incorporate large gauge invariance which implies genuinely non-perturbative finite temperature gluonic degrees of freedom. Motivated by this observation, we describe how the coupling of the Polyakov loop as an independent degree of freedom to quarks not only accounts for large gauge invariance, but also allows to establish in a dynamical way the interaction between composite hadronic states such as Goldstone bosons to finite temperature non-perturbative gluons in a medium which can undergo a confinement-deconfinement phase transition.
The aim of this work is to shed light on some lesser known aspects of Polyakov-loop--extended chiral models (namely the Polyakov-loop extended Nambu--Jona-Lasinio and Quark-Meson models), especially on the correlation of the quark sector with the Polyakov loop. We show that the ordering of chiral and Polyakov-loop transitions and their difference in temperature as seen in lattice QCD calculations could be realized with a critical scale of the Polyakov-loop potential that is larger than the one in pure gauge theory. The comparison of the results for the Polyakov-loop susceptibility obtained usi…
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using the Gocksch-Ogilvie model with fundamental or adjoint quarks. The model is based on the double expansion of strong coupling and large dimensionality on the lattice. In an analytic way with the mean field approximation employed, we show that the confined phase must be accompanied by the spontaneous breaking of the chiral symmetry for both fundamental and adjoint quarks. Then we proceed to numerical analysis to look into the coupled dynamics of the Polyakov loop and the chiral order pa…
The Polyakov loop is included in the SU(2)_L x SU(2)_R chiral quark-meson model by considering the propagation of the constituent quarks, coupled to the (sigma,pi) meson multiplet, on the homogeneous background of a temporal gauge field, diagonal in color space. The model is solved at finite temperature and quark baryon chemical potential both in the chiral limit and for the physical value of the pion mass by using an expansion in the number of flavors N_f. Keeping the fermion propagator at its tree-level, a resummation on the pion propagator is constructed which resums infinitely many orders …
Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of spherical volume decreases, the location of CEP shifts toward smaller temperature while changes little in chemical potential. As for the finite volume effects on the masses of mesons, the masses of $π$ and $K$ increase with decreasing volume, while for $σ$, $η$ and $η'$ the situation is t…
Chiral phase transition is investigated in an $SU(3)_L \times SU(3)_R$ symmetric vector meson extended linear sigma model with additional constituent quarks and Polyakov loops (extended Polyakov quark meson model). The parameterization of the Lagrangian is done at zero temperature in a hybrid approach, where the mesons are treated at tree-level, while the constituent quarks at 1-loop level. The temperature and baryochemical potential dependence of the two assumed scalar condensates are calculated from the hybrid 1-loop level equations of states. The order of the phase transition along the $T=0…
The extension of the Nambu-Jona-Lasino Model with six and eight quark interactions to include the Polyakov loop is analysed. Several interesting features are determined to be an effect of the choice of the regularization procedure. The use of a Pauli-Villars covariant regularization enables a coherent and correct description of several quantities.
We study the phase diagram of the three flavor Polyakov-Nambu-Jona Lasinio (PNJL) model and in particular the interplay between chiral symmetry restoration and deconfinement crossover. We compute chiral condensates, quark densities and the Polyakov loop at several values of temperature and chemical potential. Moreover we investigate on the role of the Polyakov loop dynamics in the transition from nuclear matter to quark matter.
We compute the transport coefficients, namely, the coefficients of shear and bulk viscosities as well as thermal conductivity for hot and dense matter. The calculations are performed within the Polyakov quark meson model. The estimation of the transport coefficients is made using the Boltzmann kinetic equation within the relaxation time approximation. The energy dependent relaxation time is estimated from meson meson scattering, quark meson scattering and quark quark scattering within the model. In our calculations, the shear viscosity to entropy ratio and the coefficient of thermal conductivi…
We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu-Jona Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently the phase diagram of the mo…
The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized 2+1 flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare 2+1 quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in quark meson linear sigma model together wit…
We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where the Lagrangian includes an interaction term that explicitly breaks the U$_A(1)$ anomaly. At finite temperature, the restoration of chiral and axial symmetries, signaled by the behavior of several observables, is investigated. We compare the effects of two regularizations at finite temperature, one of them, that allows high momentum quarks states, leading to the full recovery of chiral symmetry. From the analysis of the behavior of the topological susceptibility and of the mesonic masses of the axial partners, it is found…
We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows and the first-order transition ends in a critical endpoint. The nature of the critical endpoint is examined by studying the longitudinal and transverse fluctuations of the Polyakov loop, quantified by the corresponding susceptibilities. The longitudinal susceptibility is enhanced in the critical region, while the transverse susceptibility show…
We study the thermodynamics and phase diagrams of two-flavor quantum chromodynamics using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix ($χM$) model. At temperatures up to $T\approx2T_c$ and baryon chemical potentials up to $μ_B=400\ \rm{MeV}$, both models show reasonable agreement with the pressure, energy density, and interaction measure as calculated on the lattice. The Polyakov loop is found to rise significantly faster with temperature in models than on the lattice. In the low-temperature and high baryon density regime, the two models predict dif…
We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.
We study the spatial inhomogeneity of the Polyakov loop induced by inhomogeneous chiral condensates. We formulate an effective model of gluons on the background fields of chiral condensates, and perform its lattice simulation. On the background of inhomogeneous chiral condensates, the Polyakov loop exhibits an in-phase spatial oscillation with the chiral condensates. We also analyze the heavy quark potential and show that the inhomogeneous Polyakov loop indicates the inhomogeneous confinement of heavy quarks.
The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of Nf = 2+1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate …
The effects of the Polyakov loop and of a regularization procedure that allows the presence of high momentum quark states at finite temperature is investigated within the Polyakov-loop extended Nambu--Jona-Lasinio model. The characteristic temperatures, as well as the behavior of observables that signal deconfinement and restoration of chiral and axial symmetries, are analyzed, paying special attention to the behavior of strangeness degrees of freedom. We observe that the cumulative effects of the Polyakov loop and of the regularization procedure contribute to a better description of the therm…
We study the nucleon as a nontopological soliton in a quark medium as well as in a nucleon medium in terms of the Polyakov quark meson (PQM) model with two flavors at finite temperature and density. The constituent quark masses evolving with the temperature at various baryon chemical potentials are calculated and the equations of motion are solved according to the proper boundary conditions. The PQM model predicts an increasing size of the nucleon and a reduction of the nucleon mass in both hot environment. However, the phase structure is different from each other in quark and nucleon mediums.…
Chiral quark models with Polyakov loop at finite temperature have been often used to describe the phase transition. We show how the transition to a hadron resonance gas is realized based on the quantum and local nature of the Polyakov loop.
We describe how the coupling of the gluonic Polyakov loop to quarks solves different inconsistencies in the standard treatment of chiral quark models at finite temperature at the one quark loop level. Large gauge invariance is incorporated and an effective theory of quarks and Polyakov loops as basic degrees of freedom is generated. From this analysis we find a strong suppression of finite temperature effects in hadronic observables below the deconfinement phase transition triggered by approximate triality conservation in a phase where chiral symmetry is spontaneously broken (Polyakov cooling)…
We study the finite temperature behavior of light scalar and pseudoscalar meson properties in the context of a three-flavor nonlocal chiral quark model. The model includes mixing with active strangeness degrees of freedom, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. We analyze the chiral restoration and deconfinement transitions, as well as the temperature dependence of meson masses, mixing angles and decay constants. The critical temperature is found to be T_c = 202 MeV, in better agreement with lattice results than the value recently obta…
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.
We study the thermodynamics of QCD system under external magnetic field via the 2+1 flavor Polyakov-loop quark-meson model. To incorporate quantum and thermal fluctuations, the functional renormalization group approach is implemented in our work. Pressure, entropy density, magnetic susceptibility and other thermodynamic quantities are calculated and analyzed to investigate the effect of magnetic field on the QCD system. The calculated results are in reasonable agreement with lattice QCD simulations and perturbation theory. We then give an intuitive picture for the response of QCD system to the…
Thermodynamics and the phase structure of the Polyakov loop-extended two flavor chiral quark-meson model (PQM) are explored. The analysis of the PQM model is based on the functional renormalization group (FRG) method. An appropriate truncation of the effective action with quarks coupled to background gluonic fields is introduced. Within this scheme, we derive the renormalization group flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry breaking external field. The influence of fluctuations and of the background gluon fie…
Unquenching of the Polyakov-loop potential showed to be an important improvement for the description of the phase structure and thermodynamics of strongly-interacting matter at zero quark chemical potentials with Polyakov-loop extended chiral models. This work constitutes the first application of the quark backreaction on the Polyakov-loop potential at nonzero density. The observation is that it links the chiral and deconfinement phase transition also at small temperatures and large quark chemical potentials. The build up of the surface tension in the Polyakov-loop extended Quark-Meson model i…
Thermodynamics and the phase structure of the Polyakov loop-extended two flavors chiral quark--meson (PQM) model is explored beyond the mean-field approximation. The analysis of the PQM model is based on the functional renormalization group (FRG) method. We formulate and solve the renormalization group flow equation for the scale-dependent thermodynamic potential in the presence of the gluonic background field at finite temperature and density. We determine the phase diagram of the PQM model in the FRG approach and discuss its modification in comparison with the one obtained under the mean-fie…
NJL-type effective models represent a low-energy realization of QCD and incorporate pertinent aspects such as chiral symmetry and its spontaneous breaking, the center symmetry in the heavy-quark limit as well as the axial anomaly. One such model, the Polyakov-quark-meson model for three light quark flavors, is introduced in order to study the phase structure of strongly-interacting matter. With recent high-statistics lattice QCD simulations of the finite-temperature equation of state, a detailed comparison with model results becomes accessible. Such comparisons allow to estimate volume and tru…
We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2+1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ($T,\,μ_B$)-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change…
We study the effects of the interaction between the Chiral condensate and the Polyakov loop on the chiral transition within an effective Lagrangian. We find that the effects of the interaction change the order of the phase transition when the explicit breaking of the Z_N symmetry of the Polyakov loop is large. Our results suggest that the chiral transition in 2-flavor QCD may be first order.
The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral condensates, $σ_l$, $σ_s$ and $σ_c$ of light, strange and charm quarks, respectively and the deconfinement order-parameters $ϕ$ and $\barϕ$ at finite temperatures and densities (chemical potentials). The PLSM is considered to study the QCD equation of state in the presence of the chiral condensate of charm for different finite chemical potentials. The PLSM results are in a good agreement with the recent lattice QCD simulations. We conclude that, the charm condensate is likely not affected by the QCD phas…
In the Nambu--Jona-Lasinio model with Polyakov loops, we explore the relation between the deconfinement and chiral phase transitions within the mean-field approximation. We focus on the phase structure of the model and study the susceptibilities associated with corresponding order parameters.
We study the thermodynamics of the Nambu--Jona-Lasinio model with Polyakov loops, where spontaneous chiral symmetry breaking and confinement are taken into account. We focus on the phase structure of the model and explore the susceptibilities associated with corresponding order parameters under the mean-field approximation.
We study the relation between the continuum threshold as function of the temperature $s_0(T)$ within finite energy sum rules and the trace of the Polyakov loop $Φ$ in the framework of a nonlocal SU(2) chiral quark model, establishing a contact between both deconfinement order parameters at finite temperature $T$ and chemical potential $μ$. In our analysis, we also include the order parameter for the chiral symmetry restoration, the chiral quark condensate. We found that $s_0$ and $Φ$ providing us the same information for the deconfinement transition, both for the zero and finite chemical poten…
In the framework of the $N_f = 2+1$ flavor (axial)vector meson extended Polyakov quark meson model we investigate the QCD phase diagram at finite temperature and density. We use a $χ^2$ minimization procedure to parameterize the model based on tree\,-\,level decay widths and vacuum scalar and pseudoscalar curvature masses which incorporate the contribution of the constituent quarks. Using a hybrid approximation (mesons at tree level, fermions at one\,-\,loop level) for the grand potential we determine the phase boundary both on the $μ_B-T$ and $ρ-T$ planes. We also determine the location of th…
We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high …
We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the $μ_I$--$T$ plane where $μ_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $μ_I={1\over2}m_π$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and in the $O(2)$ universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends…
We study the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using N_tau=4 and 6 lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.
We calculate the colour averaged and colour singlet free energies of static quark anti-quark sources placed in a thermal gluonic heat bath. We discuss the renormalization of these free energies using the short distance properties of the zero temperature heavy quark potential. This leads to the definition of the renormalized Polyakov loop as an order parameter for the deconfinement phase transition of the SU(3) gauge theory which is well behaved in the continuum limit.
In an extension of the Nambu-Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net--quark number density. We also discuss how th…
The Polyakov loop extended Nambu and Jona-Lasinio model (PNJL model) in a mean field framework shows astonishingly good agreement with lattice QCD calculations which needs to be better understood. The present work reports on further developments concerning both Polyakov loop and mesonic fluctuations beyond mean field approximation. Corrections beyond mean field are of special interest for the thermal expectation values of the Polyakov loop $Φ$ and its conjugate $Φ^*$, which differ once the quark chemical potential is non-zero. Mesonic fluctuations are also considered with emphasis on the role …
We have computed shear viscosity coefficient for hot and dense QCD matter within Polyakov loop extended quark meson(PQM) model for three flavors. Viscosity coefficient is estimated using Boltzmann equation within the relaxation time approximation. Relaxation times for quarks are calculated from elastic scattering of quarks and antiquarks via gluon exchange. Also the mean free paths of strange and light quarks are estimated for this cases. The calculations are performed at finite chemical potential. Thermodynamic properties like energy, pressure, entropy densities are also computed and compared…
We analyze the chiral restoration and deconfinement transitions in the framework of a non-local chiral quark model which includes terms leading to the quark wave function renormalization, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. Non-local interactions are described by considering both a set of exponential form factors, and a set of form factors obtained from a fit to the mass and renormalization functions obtained in lattice calculations.
We present extensive studies on hot and dense quark matter with two light and one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop (so-called PNJL model). First we discuss prescription dependence in choosing the Polyakov loop effective potential and propose a simple and rather sensible ansatz. We look over quantitative comparison to the lattice measurement to confirm that the model captures thermodynamic properties correctly. We then analyze the phase structure with changing the temperature, quark chemical potential, quark masses, and coupling constants. We particularly in…
