We present results of a simulation of two flavor QCD on a 16 3 ×4 lattice using p4-improved staggered fermions with bare quark mass m/T = 0.4. Derivatives of the thermodynamic grand canonical partition function Z(V, T, µ u , µ d ) with respect to chemical potentials µ u,d for different quark flavors are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of µ q = (µ u + µ d )/2 via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergence of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nτ = 8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a 2 ) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nτ = 6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV.

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential . Derivatives of quark and gluonic observables with respect to are computed at ϭ0 for two flavors of p4 improved staggered fermions with maϭ0.1,0.2 on a 16 3 ϫ4 lattice, and used to calculate the leading order Taylor expansion in of the location of the pseudocritical point about ϭ0. This expansion should be well behaved for the small values of q /T c ϳ0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T c () in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of 0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with 0.

We present results of a simulation of QCD on a 16 3 × 4 lattice with 2 continuum flavors of p4-improved staggered fermion with mass m/T = 0.4. Derivatives of the thermodynamic grand potential Ω with respect to quark chemical potential µ q up to fourth order are calculated, enabling estimates of the pressure, quark number density and associated susceptibilities as functions of µ q via Taylor series expansion. Discretisation effects associated with various staggered fermion formulations are discussed in some detail. In addition it is possible to estimate the radius of convergence of the expansion as a function of temperature. We also discuss the calculation of energy and entropy densities which are defined via mixed derivatives of Ω with respect to the bare couplings and quark masses.