  Supplementing the holographic Einstein-Maxwell-dilaton model of [O. DeWolfe,
S.S. Gubser, C. Rosen, Phys. Rev. D83 (2011) 086005; O. DeWolfe, S.S. Gubser,
C. Rosen, Phys. Rev. D84 (2011) 126014] by input of lattice QCD data for 2+1
flavors and physical quark masses for the equation of state and quark number
susceptibility at zero baryo-chemical potential we explore the resulting phase
diagram over the temperature-chemical potential plane. A first-order phase
transition sets in at a temperature of about 112 MeV and a baryo-chemical
potential of 612 MeV. We estimate the accuracy of the critical point position
in the order of approximately 5-8% by considering parameter variations and
different low-temperature asymptotics for the second-order quark number
susceptibility. The critical pressure as a function of the temperature has a
positive slope, i.e. the entropy per baryon jumps up when crossing the phase
border line from larger values of temperature/baryo-chemical potential, thus
classifying the phase transition as a gas liquid one. The updated holographic
model exhibits in- and outgoing isentropes in the vicinity of the first-order
phase transition.
