Reentrant Phase Transitions and van der Waals Behaviour for Hairy Black Holes

We study the extended phase space thermodynamics for hairy AdS black hole solutions to Einstein-Maxwell- theory conformally coupled to a scalar field in five dimensions. We find these solutions to exhibit van der Waals behaviour in both the charged/uncharged cases, and reentrant phase transitions in the charged case. This is the first example of reentrant phase transitions in a five dimensional gravitational system which does not include purely gravitational higher curvature corrections.