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The chiral critical surface is a surface of second order phase transitions bounding the region of first order chiral phase transitions for small quark masses in the {m_{u,d}, m_s,\mu} parameter space. The potential critical endpoint of the…
This is a pedagogical review of some recent progress in rigorously proving chiral symmetry breaking in a class of QCD-like theories that closely resemble the real-world QCD, namely the $SU(N_c)$ Yang-Mills theory coupled to $N_f$ flavors of…
QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although sign-free QCD-like theories have been studied…
From the non-extensive statistical mechanics, we investigate the chiral phase transition at finite temperature $T$ and baryon chemical potential $\mu_B$ in the framework of the linear sigma model. The corresponding non-extensive…
We investigate a nonlocal chiral quark model with separable 4-fermion interaction for the case of U(3) flavor symmetry and show that strange quark matter is unlikely to occur in a large enough volume of a compact star to entail remarkable…
A qualitative analysis of the chiral phase transition in QCD with two massless quarks and non-zero baryon density is performed. It is assumed that at zero baryonic density, $\rho=0$, the temperature phase transition is of the second order…
In heavy ion collision experiments as well as in neutron stars, both baryon and isospin chemical potentials are different from zero. In particular, the regime of small isospin chemical potential is phenomenologically important. Using a…
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…
We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(Nc) gauge…
We study the chiral phase transition at finite $T$ and $\mu_B$ within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential…
The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents…
I review arguments for the existence of a critical point in the QCD phase diagram as a function of temperature and baryon chemical potential. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale…
We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $\mu_{X=B,Q,S,I}$. The results were…
Quenched QCD at zero baryonic chemical potential undergoes a first-order deconfinement phase transition at a critical temperature $T_c$, which is related to the spontaneous breaking of the global center symmetry. Including heavy, dynamical…
Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass have remained inconclusive because of their…
Common lore suggests that $N$-color QCD with massive quarks has no useful order parameters which can be non-trivial at zero baryon density. However, such order parameters do exist when there are $n_f$ quark flavors with a common mass and…
Quantum chromodynamics (QCD) at finite temperature, $T$, and quark chemical potential, $\mu$, has a rich phase structure: at low $T$ and low $\mu$, the Nambu-Goldstone (NG) phase with nearly massless pions is realized by the dynamical…
We study the phase transition between pion condensed phase and normal phase, as well as chiral phase transition in a two flavor($\mathcal{N}_f=2$) IR- improved soft-wall AdS/QCD model at finite isospin chemical potential $\mu_I$ and…
We use the linear sigma model with two flavors of quarks to study the phase diagram at finite temperature and baryon chemical potential as a function of the vacuum pion mass. Our calculations include thermal fluctuations of both the bosonic…
We study the chemical potential effects on the chiral phase transition in a simply improved soft-wall AdS/QCD model, which can realize consistently the properties of linear confinement and spontaneous chiral symmetry breaking. The $\mu-T$…