Tricritical point and solid/liquid/gas phase transition of higher dimensional AdS black hole in massive gravity

By considering the fifth order term of the interaction potential in massive gravity theory, we study the $P-V$ critical behaviors of AdS black hole in $d \geq 7$ dimensional space-time, and find the tricritical point and the solid/liquid/gas phase transition in addition to the Van der Waals-like phase and the reentrant phase transition of the system. The critical phenomena of black holes depend crucially on the number $n$ of interaction potential terms.