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