QCD thermodynamics with effective models

In this talk we extend the Polyakov-quark-meson model to N_f=2+1 quark flavors and study its bulk thermodynamics at finite temperatures in mean-field approximation. Three different Polyakov-loop potentials are considered. Our findings are confronted to recent QCD lattice simulations of the RBC-Bielefeld and HotQCD collaborations. Furthermore, the finite chemical potential expansion of the quark-number susceptibility in a Taylor series around vanishing chemical potential is analyzed. By means of a novel algorithmic differentiation technique, we have calculated Taylor coefficients up to 24th order in the model for the first time. This allows the systematic study of convergence properties of the Taylor series.Comment: [references added]; 10 pages, 5 figures, talk given at the workshop CPOD 2009, June 08 - 12, BNL, US

On the efficient computation of high-order derivatives for implicitly defined functions

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order derivatives. A technique based on algorithmic differentiation is presented which allows for a precise calculation of higher-order derivatives. The method can be widely applied even for the case of only numerically solvable, implicit dependencies which totally hamper a semi-analytical calculation of the derivatives. As a demonstration the method is applied to a quantum field theoretical physical model. The results are compared with standard numerical derivative methods.Comment: 11 pages, 4 figures, to appear in Comput. Phys. Commu

QCD Green's Functions and Phases of Strongly-Interacting Matter

After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green's functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-)confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de-)confinement and dynamical chiral symmetry breaking (restoration). Last but not least some results of Dyson-Schwinger equations for the color-superconducting phase at large densities are shown.Comment: 8 pages, 5 figures; talk at the International Workshop on Hot & Cold Baryonic Matter, 15-20 August 2010, Budapest - Hungar

QCD Thermodynamics: Confronting the Polyakov-Quark-Meson Model with Lattice QCD

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 truncation effects of quantities, obtained on the lattice and provide possible lattice extrapolation procedures to finite chemical potential which are important to locate a critical endpoint in the QCD phase diagram.Comment: 10 pages, 4 figures, contributed to the proceedings of the EMMI Workshop and XXVI Max Born Symposium at 09th-11th of July 2009 in Wroclaw, Polan

Center Phase Transition from Fundamentally Charged Matter Propagators

The center phase transition at non-vanishing temperatures is investigated in Landau gauge Quantum Chromodynamics (QCD) and scalar QCD. For each theory novel order parameters for the transition are introduced. The matter-gluon vertex which occurs in the Dyson-Schwinger equations of the propagators has to be modeled in contemporary studies. It is found that the nature of the phase transition depends strongly on the detailed structure of this vertex. Our investigation motivates a precise determination of the matter-gluon vertex at non-vanishing temperatures.Comment: 8 pages, Confinement X proceeding

On the phase structure and thermodynamics of QCD

We discuss the phase structure and thermodynamics of QCD by means of dynamical chiral effective models. Quark and meson fluctuations are included via the functional renormalization group. We study the influence of confinement in addition to the impact of fluctuations by comparing the results of the chiral models to their Polyakov-loop extended versions. Furthermore, we discuss the mass sensitivity of the phase structure and thermodynamics and find interesting modifications close to the chiral limit.Comment: 13 pages, 11 figures; Appendix added; published versio