  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.
