Over the past few years new physics methods and algorithms as well as the latest supercomputers have enabled the study of the QCD thermodynamic phase transition using lattice gauge theory numerical simulations with unprecedented control over systemat
ic errors. This is largely a consequence of the ability to perform continuum extrapolations with physical quark masses. Here we review recent progress in lattice QCD thermodynamics, focussing mainly on results that benefit from the use of physical quark masses: the crossover temperature, the equation of state, and fluctuations of the quark number susceptibilities. In addition, we place a special emphasis on calculations that are directly relevant to the study of relativistic heavy ion collisions at RHIC and the LHC.
We present results from recent calculations of the QCD equation of state by the HotQCD Collaboration and review the implications for hydrodynamic modeling. The equation of state of QCD at zero baryon density was calculated on a lattice of dimensions
$32^3 times 8$ with $m_l = 0.1 m_s$ (corresponding to a pion mass of $sim$220 MeV) using two improved staggered fermion actions, p4 and asqtad. C alculations were performed along lines of constant physics using more than 100M cpu-hours on BG/L supercomputers at LLNL, NYBlue, and SDSC. We present paramete rizations of the equation of state suitable for input into hydrodynamics models of heavy ion collisions.
