  In this paper, we present an AdS black hole solution with Ricci flat horizon
in Einstein-phantom scalar theory. The phantom scalar fields just depend on the
transverse coordinates $x$ and $y$, and which are parameterized by the
parameter $\alpha$. We study the thermodynamics of the AdS phantom black hole.
Although its horizon is a Ricci flat Euclidean space, we find that the
thermodynamical properties of the black hole solution are qualitatively same as
those of AdS Schwarzschild black hole. Namely there exists a minimal
temperature, the large black hole is thermodynamically stable , while the
smaller one is unstable, so there is a so-called Hawking-Page phase transition
between the large black hole and the thermal gas solution in the AdS spacetime
in Poincare coordinates. We also calculate the entanglement entropy for a strip
geometry dual to the AdS phantom black holes and find that the behavior of the
entanglement entropy is qualitatively the same as that of the black hole
thermodynamical entropy.
