  We present a new family of asymptotically AdS four-dimensional black hole
solutions with scalar hair of a gravitating system consisting of a scalar field
minimally coupled to gravity with a self-interacting potential. For a certain
profile of the scalar field we solve the Einstein equations and we determine
the scalar potential. Thermodynamically we show that there is a critical
temperature below which there is a phase transition of a black hole with
hyperbolic horizon to the new hairy black hole configuration.
