Lattice Regularized QCD at Finite Temperature

During the first part of this review we will focus on the thermodynamics of $SU(N)$ gauge theories at finite temperature. We will present results from a calculation of electric and magnetic screening masses for the gluons, discuss calculations of the critical temperature in units of the string tension and bulk thermodynamic quantities like the energy density and pressure. In particular, the latter calculations have now reached a stage where $O(a^2)$ cut-off effects can be controlled systematically and an extrapolation to the continuum limit can be performed. In the second part we discuss the critical behaviour of QCD with light quarks. We analyze the chiral transition in 2-flavour QCD and present results on the temperature dependence of hadron properties.Comment: 20 pages, 13 Postscript figure

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<Tc, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below Tc and diverges like 1/sqrt(m_l) in the chiral limit.Comment: 4 pages,presented in Strong and ElectroWeak Matter, August 2008, Amsterdam, The Netherland

Thermodynamics of 2 and 3 flavour QCD

We discuss recent results on the thermodynamics of QCD in the presence of light dynamical quark degrees of freedom. In particular, we concentrate on an analysis of the flavour and quark mass dependence of the QCD phase diagram, the equation of state and the transition temperature. Moreover, we present recent results on the heavy quark free energy.Comment: 10 pages, To appear in the proceedings of QCD@Work: International Conference on QCD: Theory and Experiment, Martina Franca, Italy, 16-20 Jun 200

QCD thermodynamics in the crossover/freeze-out region

We use results from a 6-th order Taylor expansion of the QCD equation of state to construct expansions for cumulants of conserved charge fluctuations and their correlations. We show that these cumulants strongly constrain the range of applicability of hadron resonance gas model calculations. We point out that the latter is inappropriate to describe equilibrium properties of QCD at zero and non-zero values of the baryon chemical potential already at T~155 MeV.Comment: 5 pages, 6 figures, contribution to the International Conference "Critical Point and Onset of Deconfinement 2016", Wroc{\l}aw, Poland, May 30th - June 4th, 201

Lattice Simulations of the Thermodynamics of Strongly Interacting Elementary Particles and the Exploration of New Phases of Matter in Relativistic Heavy Ion Collisions

At high temperatures or densities matter formed by strongly interacting elementary particles (hadronic matter) is expected to undergo a transition to a new form of matter - the quark gluon plasma - in which elementary particles (quarks and gluons) are no longer confined inside hadrons but are free to propagate in a thermal medium much larger in extent than the typical size of a hadron. The transition to this new form of matter as well as properties of the plasma phase are studied in large scale numerical calculations based on the theory of strong interactions - Quantum Chromo Dynamics (QCD). Experimentally properties of hot and dense elementary particle matter are studied in relativistic heavy ion collisions such as those currently performed at the relativistic heavy ion collider (RHIC) at BNL. We review here recent results from studies of thermodynamic properties of strongly interacting elementary particle matter performed on Teraflops-Computer. We present results on the QCD equation of state and discuss the status of studies of the phase diagram at non-vanishing baryon number density.Comment: 10 pages, invited plenary talk given at the conference 'Scientific Discovery through Advanced Computing', SciDAC 2006, June 25-29, Denver, US

O(N) universality and the chiral phase transition in QCD

We discuss universal scaling properties of (2+1)-flavor QCD in the vicinity of the chiral phase transition at vanishing as well as non-vanishing light quark chemical potential (mu_l). We provide evidence for O(N) scaling of the chiral order parameter in (2+1)-flavor QCD and show that the scaling analysis of its derivative with respect to the light quark chemical potential provides a unique approach to the determination of the curvature of the chiral phase transition line in the vicinity of mu_l/T=0.Comment: 6 pages, 6 EPS-files; talk presented at the International Workshop 'New Frontiers in QCD 2010' at the Yukawa Institute for Theoretical Physics, Kyoto, Japan, March 1-1

Deconfinement and Quarkonium Suppression

Modifications in the production pattern of heavy quark bound states have long been considered to provide sensitive signatures for the thermal properties of dense matter created in heavy ion collisions. The original concept of Matsui and Satz for quarkonium suppression as signature for deconfinement in heavy ion collisions has been challenged recently through lattice studies of spectral functions, which indicate the persistence of heavy quark bound states at temperatures well above the transition, as well as through the refined analysis of hadronization and recombination models, which take into account the thermal evolution of the medium generated in a heavy ion collision. We will review here recent developments on these topics.Comment: 10 pages, contribution to the proceedings of Hard Probes 2004, International Conference on Hard and Electromagnetic Probes of High Energy Nuclear Collisions, Nov. 4-10, 2004, Ericeira, Portugal, references update

Lattice QCD at High Temperature and the QGP

We review recent progress in studies of bulk thermodynamics of strongly interacting matter, present results on the QCD equation of state and discuss the status of studies of the phase diagram at non-vanishing quark chemical potential.Comment: 9 pages, plenary talk given at PANIC05, Particles and Nuclei International Conference, Santa Fe, NM, Oct. 24-28, 200