The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

Resonance states in an effective chiral hadronic model

With an effective chiral flavour SU(3) model we show the effect of hadronic resonances on the QCD phase diagram. We state that varying the resonance couplings to the scalar and vector fields affects the order and location of the phase transition, the possible existence of a critical end point (CEP), and the thermodynamic properties. We present (strange) quark number susceptibilities at zero baryochemical potential and at three different points at the phase transition. Comparing results to lattice QCD, we state that reasonable large vector couplings limit the phase transition to a smooth crossover ruling out a CEP.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Fluctuations and the QCD phase diagram

In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.     

Lattice QCD with chemical potential: Evading the fermion-sign problem

Since the turn of the millennium there has been tremendous progress in understanding QCD at finite chemical potential, μ. Apart from qualitative results obtained using models, and exact results at very large μ obtained in weak coupling theory, there has been tremendous progress in getting exact and quantitative results from lattice simulations. I summarize the status of lattice QCD at finite chemical potential —locating the critical end-point in the QCD phase diagram, predicting event-to-event fluctuation rates of conserved quantities, and finding the rate of strangeness production.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

Dyson-Schwinger approach to color superconductivity at finite temperature and density

We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N _f = 2 + 1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop-hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20–30 MeV, the critical temperatures to the normal phase turn out to be quite small.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T _?? = 152.9 ± 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T _?? defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result but is quite familiar for ordinary liquids at the supercritical temperatures.     

Analysis of the Migdal transformation for models with planar spins on a d-dimensional lattice

We show analytically that in the Migdal approximation and at low temperatures planar spins on a d-dimensional lattice (d ⩾ 2) exhibit the same phase transitions as d-dimensional Z(n)-models. For a three-dimensional lattice part of the flow diagram of the Migdal mapping is found numerically, including large families of relevant fixed points which separate the low-temperature fixed points from the trivial high-temperature one. The critical exponents are obtained and for some two-parameter potentials the phase diagram is constructed and explained. After rescaling, quantitative agreement was obtained for one of the Migdal phase diagrams with the Monte Carlo phase diagram.     

Noncritical holographic QCD in external electric field

We investigate behavior of a noncritical model in external electric field and explore its phase structure in the quenched approximation Nf?Nc. We compute the conductivity of QCD plasma in this model and compare it with the predictions of Sakai-Sugimoto model, D3-D7 system and lattice simulations. We find that, while the behavior of conductivity in noncritical model as a function of temperature and baryon density is similar to those of D3-D7 system, the phase diagram of noncritical model resembles the phase diagram of Sakai-Sugimoto model.     

Towards finite density QCD with Taylor expansions

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.     

QCD at a Finite isospin density: From the pion to quark-antiquark condensation

QCD at a finite isospin chemical potential μ _I is studied. This theory has no fermion-sign problem and can be simulated on a lattice by using present-day techniques. We solve this theory analytically in two limits: low μ _I, where chiral perturbation theory is applicable, and asymptotically high μ _I, where perturbative QCD is at work. At a low isospin density, the ground state is a superfluid pion condensate. At a very high density, it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture passes several nontrivial tests. Our results imply a nontrivial phase diagram in the space of the temperature and chemical potentials of isospin and baryon number. At asymptotically large values of μ _I and small values of the baryon chemical potential, the ground state is in a phase similar to the Fulde-Ferrell-Larkin-Ovchinnikov phase. It is characterized by a spatially modulated superfluid order parameter 〈ūγ ₅ d〉 and may be the asymptotic limit of the inhomogeneous pion-condensation phase advocated by Migdal and others.     

Dynamical generation of a Coulomb phase in the mean-field approach to Z(N) lattice gauge theories

The phase diagram of Z(N) lattice gauge theories is examined in the mean-field approach. It is shown how large non-perturbative fluctuations around the mean-field may naturally occur in these theories. When this happens, a massless phase which is absent in the mean-field approximation is dynamically generated. An order parameter which characterizes the Coulomb to Higgs phase transition is introduced. The predictions for the values of the critical coupling for this transition are in excellent agreement with the Monte Carlo data in four dimensions.     

Critical behavior of the one-dimensional commensurate-incommensurate transition

We study the low-temperature critical behavior of one-dimensional charge-density-waves coupled to an underlying lattice, using the McMillan free energy. For weak coupling, the incommensurate CDW orders at T = 0 as a lattice of phase slip solutions with XY critical behavior. For strong coupling, the commensurate CDW orders at T = 0 with Ising critical behavior. Analytic expressions for the low-temperature inverse correlation length and average phase change are obtained for all values of the coupling to the lattice.     

Vector Meson Mass in Finite Density and Temperature Lattice QCD

Vector meson mass values are studied at finite chemical potential and temperature in lattice QCD with lattice size of 24 × 122× 6 using two flavors of staggered quarks. The investigation focuses on the change of the vector meson mass in the critical region close to T c with two different types of chemical potentials switched on: the isoscalar chemical potential μS and its isovector counterpart μV. It is found that the vector meson mass increases in the QGP phase with both chemical potentials and decreases with μS in the confinement phase.     

Phase diagram and phase transitions of the adsorbate system S/Ru(0001): a Monte Carlo study of a lattice gas model

We investigate the phase diagram and the critical properties of the adsorbate system sulphur/ruthenium(0001) in the coverage region 0 < Θ < 1/3 using Monte Carlo simulations of a lattice gas model on a triangular lattice. From experiments it is known that for low coverages an island phase appears in the phase diagram of this system at low temperatures. To capture this feature we include in our lattice gas model a weak third neighbour attraction in addition to the repulsive first and second neighbour forces. The phase diagram obtained from simulations of this model is in very good agreement with the experimental phase diagram. The critical properties of the lattice gas model are found to be compatible with the results of experiments on the system sulphur/ruthenium(0001). Finer details of the phase diagram, e. g. the location of tricritical points, which may be difficult to assess experimentally will also be discussed.