Thermodynamics of charged black holes in Maxwell-dilaton-massive gravity

Considering the nonminimal coupling of the dilaton field to the massive graviton field in Maxwell-dilaton-massive gravity, we obtain a class of analytical solutions of charged black holes, which are neither asymptotically flat nor (A)dS. The calculated thermodynamic quantities, such as mass, temperature, and entropy, verify the validity of the first law of black hole thermodynamics. Moreover, we further investigate the critical behaviors of these black holes in the grand canonical and canonical ensembles and find a novel critical phenomenon never before observed, known as the "reverse" reentrant phase transition with a tricritical point. It implies that the system undergoes a novel "SBH-LBH-SBH" phase transition process and is the reverse of the "LBH-SBH-LBH" process observed in reentrant phase transitions.