  By using the AdS/CFT correspondence, we construct an Einstein-Maxwell-Dilaton
model to map the thermodynamics of strongly interacting matter. The holographic
model, constrained to reproduce the lattice QCD equation of state at zero
baryon chemical potential, predicts a critical end point and a first order
phase transition line. We also obtain the equation of state of the model for a
large region of the phase diagram. We characterize the crossover transition
region by two lines, one associated to the inflection of the second order
baryon susceptibility, and another one associated to the minimum of the square
of the speed of sound along trajectories of constant entropy per baryon number.
We observe that both lines merge at the critical point.
