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We provide an exact hairy black hole solution to an $n+1$ dimensional complexscalar field model coupled with gravity. The model is characterized by apotential with one parameter. Depending on the magnitude of this parameter, theeffective mass square of the scalar field can be both positive and negative. Nomatter what case it is, there are temperature ranges in which the hairy blackhole is thermodynamically stable against decaying into its no-hair counterpart.We use this solution as an AdS/CFT superconductor model and study itsconductivity-frequency relation and find typical features observed in otherAdS/CFT superconductor models.

An Exact Hairy Black Hole Solution for AdS/CFT Superconductors