Recent result in QCD thermodynamics from the lattice

Recent results on QCD thermodynamics are presented. The nature of the T>0 transition is determined, which turns out to be an analytic cross-over. The absolute scale for this transition is calculated. The results were obtained by using a Symanzik improved gauge and stout-link improved fermionic action. In order to approach the continuum limit four different sets of lattice spacings were used with temporal extensions N_t =4, 6, 8 and 10 (they correspond to lattice spacings a∼0.3, 0.2, 0.15 and 0.12 fm). The equation of state is determined on N_t =4 and 6 lattices. The importance of the continuum limit for different results (critical endpoint, colour superconducting phase) at non-vanishing baryonic densities is discussed.