A status of lattice QCD thermodynamics, as of 2013, is summarized. Only bulk thermodynamics is considered. There is a separate section on magnetic fields.
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.
The thesis will present results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of t
he quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used.
We present results for the equation of state upto previously unreachable, high temperatures. Since the temperature range is quite large, a comparison with perturbation theory can be done directly.
