Abstract:
The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extension $N_t=4$. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.

Abstract:
I review our current understanding of the properties of strongly interacting matter at high temperatures, based upon numerical calculations in lattice QCD. I discuss the chiral and deconfining aspects of the QCD transition, the equation of state, fluctuations of conserved charges, color screening, meson correlation functions, and the determination of some transport coefficients.

Abstract:
We investigate the lattice QCD Dirac operator with staggered fermions at temperatures around the chiral phase transition. We present evidence of a metal-insulator transition in the low lying modes of the Dirac operator around the same temperature as the chiral phase transition. This strongly suggests the phenomenon of Anderson localization drives the QCD vacuum to the chirally symmetric phase in a way similar to a metal-insulator transition in a disordered conductor. We also discuss how Anderson localization affects the usual phenomenological treatment of phase transitions a la Ginzburg-Landau.

Abstract:
After a brief introduction into basic aspects of the formulation of lattice regularized QCD at finite temperature and density we discuss our current understanding of the QCD phase diagram at finite temperature. We present results from lattice calculations that emphasize the deconfining as well as chiral symmetry restoring features of the QCD transition, and discuss the thermodynamics of the high temperature phase.

Abstract:
We study the chiral phase transition with staggered fermions on the lattice at finite temperature in the strong coupling limit. The thermodynamic potential is derived in the large $d$ approximation where $d+1$ is the dimension of space time. Our calculation is simpler than the conventional method and leads to a simple physical interpretation for the approximation scheme.

Abstract:
We present evidence that in full QCD with two dynamical quarks confinement is produced by dual superconductivity of the vacuum as in the quenched theory. Preliminary information is obtained on the nature of the deconfining transition.

Abstract:
We discuss the critical behaviour of strongly interacting matter close to the QCD phase transition. Emphasis is put on a presentation of results from lattice calculations that illustrate deconfining as well as chiral symmetry restoring features of the phase transition. We show that both transitions coincide in QCD while they fall apart in an SU(3) gauge theory coupled to adjoint fermions. We also discuss some results on deconfinement in quenched QCD at non-zero baryon number.

Abstract:
QCD with 2 flavours of massless colour-sextet quarks is studied as a possible walking-Technicolor candidate. We simulate the lattice version of this model at finite temperatures near to the chiral-symmetry restoration transition, to determine whether it is indeed a walking theory (QCD-like with a running coupling which evolves slowly over an appreciable range of length scales) or if it has an infrared fixed point, making it a conformal field theory. The lattice spacing at this transition is decreased towards zero by increasing the number $N_t$ of lattice sites in the temporal direction. Our simulations are performed at $N_t=4,6,8,12$, on lattices with spatial extent much larger than the temporal extent. A range of small fermion masses is chosen to make predictions for the chiral (zero mass) limit. We find that the bare lattice coupling does decrease as the lattice spacing is decreased. However, it decreases more slowly than would be predicted by asymptotic freedom. We discuss whether this means that the coupling is approaching a finite value as lattice $N_t$ is increased -- the conformal option, or if the apparent disagreement with the scaling predicted by asymptotic freedom is because the lattice coupling is a poor expansion parameter, and the theory walks. Currently, evidence favours QCD with 2 colour-sextet quarks being a conformal field theory. Other potential sources of disagreement with the walking hypothesis are also discussed. We also report an estimate of the position of the deconfinement transition for $N_t=12$, needed for choosing parameters for zero-temperature simulations.

Abstract:
The determination of the parameters of the deconfining transition in N_f=2 QCD is discussed, and its relevance to the understanding of the mechanism of color confinement.

Abstract:
We study the finite density phase transition in the lattice QCD at real chemical potential. We adopt canonical approach and the canonical partition function is constructed for Nf=2 QCD. After derivation of the canonical partition function we calculate observables like the pressure, the quark number density, its second cumulant and the chiral condensate as a function of the real chemical potential. We covered a wide range of temperature region starting from the confining low to the deconfining high temperature. We observe signals for the deconfinement and the chiral restoration phase transition at real chemical potential below Tc starting from the confining phase.