The present paper concludes our investigation on the QCD equation of state with 2+1 staggered flavors and one-link stout improvement. We extend our previous study [JHEP 0601:089 (2006)] by choosing even finer lattices. Lattices with $N_t=6,8$ and 10 are used, and the continuum limit is approached by checking the results at $N_t=12$. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We use physical quark masses, that is, for the lightest staggered pions and kaons we fix the $m_\pi/f_K$ and $m_K/f_K$ ratios to their experimental values. The pressure, the interaction measure, the energy and entropy density and the speed of sound are presented as functions of the temperature in the range $100 ...1000 \textmd{MeV}$. We give estimates for the pion mass dependence and for the contribution of the charm quark. We compare our data to the equation of state obtained by the "hotQCD" collaboration.Comment: Minor changes: Figure 1 added; Figure 15, Figure 17 and Table 5 changed. Accepted for publication in JHE

The effect of an external (electro)magnetic field on the finite temperature transition of QCD is studied. We generate configurations at various values of the quantized magnetic flux with N f = 2 + 1 flavors of stout smeared staggered quarks, with physical masses. Thermodynamic observables including the chiral condensate and susceptibility, and the strange quark number susceptibility are measured as functions of the field strength. We perform the renormalization of the studied observables and extrapolate the results to the continuum limit using N t = 6, 8 and 10 lattices. We also check for finite volume effects using various lattice volumes. We find from all of our observables that the transition temperature T c significantly decreases with increasing magnetic field. This is in conflict with various model calculations that predict an increasing T c (B). From a finite volume scaling analysis we find that the analytic crossover that is present at B = 0 persists up to our largest magnetic fields eB ≈ 1 GeV 2 , and that the transition strength increases mildly up to this eB ≈ 1 GeV 2 .

We extend our previous study [Phys. Lett. B643 (2006) 46] of the crossover temperatures (T c ) of QCD. We improve our zero temperature analysis by using physical quark masses and finer lattices. In addition to the kaon decay constant used for scale setting we determine four quantities (masses of the Ω baryon, K * (892) and φ(1020) mesons and the pion decay constant) which are found to agree with experiment. This implies that -independently of which of these quantities is used to set the overall scale-the same results are obtained within a few percent. At finite temperature we use finer lattices down to a < ∼ 0.1 fm (N t = 12 and N t = 16 at one point). Our new results confirm completely our previous findings. We compare the results with those of the 'hotQCD' collaboration.