  We investigate consistent charged black hole solutions to the
Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The
solutions are gravity duals to phases of a non-conformal plasma at finite
temperature and density. For the dilaton we take a quadratic ansatz leading to
linear confinement at zero temperature and density. We consider a grand
canonical ensemble, where the chemical potential is fixed, and find a rich
phase diagram involving the competition of small and large black holes. The
phase diagram contains a critical line and a critical point similar to the van
der Waals-Maxwell liquid-gas transition. As the critical point is approached,
we show that the trace anomaly in the plasma phases vanishes signifying the
restoration of conformal symmetry in the fluid. We find that the heat capacity
and charge susceptibility diverge as $C_V \propto (T-T^c)^{-\alpha}$ and $\chi
\propto (T-T^c)^{-\gamma}$ at the critical point with universal critical
exponents $\alpha=\gamma=2/3$. Our results suggest a description of the
thermodynamics near the critical point in terms of catastrophe theories. In the
limit $\mu \to 0$ we compare our results with lattice results for $SU(N_c)$
Yang-Mills theories.
