Thermodynamics and phase structure of an Einstein-Maxwell-scalar model in extended phase space

In this paper, we study thermodynamics and phase structure of asymptotically AdS hairy and Reissner-Nordström-AdS (RNAdS) black holes in the extended phase space, where the cosmological constant is interpreted as a thermal pressure. The RNAdS and hairy black holes are black hole solutions of an Einstein-Maxwell-scalar (EMS) model with a nonminimal coupling between the scalar and electromagnetic fields. The Smarr relation, the first law of thermodynamics and the free energy are derived for black hole solutions in the EMS model. Moreover, the phase structure of the RNAdS and hairy black holes is investigated in canonical and grand canonical ensembles. Interestingly, RNAdS BH/hairy BH/RNAdS BH reentrant phase transitions, consisting of zeroth-order and second-order phase transitions, are found in both ensembles.