Lattice QCD at finite temperature and density

QCD at finite temperature and density is becoming increasingly important for various experimental programmes, ranging from heavy ion physics to astro-particle physics. The non-perturbative nature of non-abelian quantum field theories at finite temperature leaves lattice QCD as the only tool by which we may hope to come to reliable predictions from first principles. This requires careful extrapolations to the thermodynamic, chiral and continuum limits in order to eliminate systematic effects introduced by the discretization procedure. After an introduction to lattice QCD at finite temperature and density, its possibilities and current systematic limitations, a review of present numerical results is given. In particular, plasma properties such as the equation of state, screening masses, static quark free energies and spectral functions are discussed, as well as the critical temperature and the QCD phase structure at zero and finite density.Comment: 32 pages, typos corrected, reference added. Lectures given at 45. Internationale Universitatswochen fur Theoretische Physik: (Schladming Winter School on Theoretical Physics): Conceptual and Numerical Challenges in Femto-Scale and Peta-Scale Physics, Schladming, Styria, Austria, 24 Feb - 3 Mar 200

QCD at Non-Zero Density : Lattice Results

A concise review of the progress of lattice calculations at non-zero density since QM2006 is given, with emphasis on the high baryon density, low temperature domain. Possibilities for exploring densities higher than those studied by standard techniques are analysed. The phase transitions of cold, dense matter, where the sign problem remains severe, are discussed in the context of QCD-like models and approximations to QCD.Comment: 8 pages, 8 figures. Plenary talk at Quark Matter 2008: 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM2008), Jaipur, India, 4-10 Feb 2008. Pdflatex problem fixe

Lattice QCD at finite density

QCD at finite density presents specific challenges to lattice gauge theory. Nonetheless, a region of the QCD phase diagram up to moderately large baryon chemical potentials has been successfully explored on the lattice and new results and idea are continuously emerging. I will outline the lattice formulation of QCD, introduce the calculational schemes currently used to treat a nonzero baryon density, and mention lattice methods alternative to MonteCarlo, including the strong coupling expansion which might give access to the the superconducting phase of QCD. The results for the critical line, and the different phases will be discussed highlighting the strength of the different methods, as well as the possible comparisons with phenomenological models.Comment: 14 pages; to appear in the proceedings of Workshop on Finite Density QCD at Nara, Nara, Japan, 10-12 July 200

An introduction to lattice QCD at non--zero temperature and density

This is an informal overview of methods and results on the QCD phase diagram and lattice termodynamics aimed at specialists in nearby fields.Comment: 15 pages; lecture at the GISELDA Meeting held in Frascati, Italy, 14-18 January 200

Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks

We present the first results for lattice QCD at finite temperature $T$ and chemical potential $\mu$ with four flavors of Wilson quarks. The calculations are performed using the imaginary chemical potential method at $\kappa=0$, 0.001, 0.15, 0.165, 0.17 and 0.25, where $\kappa$ is the hopping parameter, related to the bare quark mass $m$ and lattice spacing $a$ by $\kappa=1/(2ma+8)$. Such a method allows us to do large scale Monte Carlo simulations at imaginary chemical potential $\mu=i \mu_I$. By analytic continuation of the data with $\mu_I < \pi T/3$ to real values of the chemical potential, we expect at each $\kappa\in [0,\kappa_{chiral}]$, a transition line on the $(\mu, T)$ plane, in a region relevant to the search for quark gluon plasma in heavy-ion collision experiments. The transition is first order at small or large quark mass, and becomes a crossover at intermediate quark mass.Comment: Published versio