  We consider the critical behaviors and phase transitions of Gauss Bonnet-Born
Infeld-AdS black holes (GB-BI-AdS) for $d=5,6$ and the extended phase space. We
assume the cosmological constant, $\Lambda$, the coupling coefficient $\alpha$,
and the BI parameter $\beta$ to be thermodynamic pressures of the system.
Having made these assumptions, the critical behaviors are then studied in the
two canonical and grand canonical ensembles. We find "reentrant and triple
point phase transitions" (RPT-TP) and "multiple reentrant phase transitions"
(multiple RPT) with increasing pressure of the system for specific values of
the coupling coefficient $\alpha$ in the canonical ensemble. Also, we observe a
reentrant phase transition (RPT) of GB-BI-AdS black holes in the grand
canonical ensemble and for $d=6$. These calculations are then expanded to the
critical behavior of Born-Infeld-AdS (BI-AdS) black holes in the third order of
Lovelock gravity and in the grand canonical ensemble to find a Van der Waals
behavior for $d=7$ and a reentrant phase transition for $d=8$ for specific
values of potential $\phi$ in the grand canonical ensemble. Furthermore, we
obtain a similar behavior for the limit of $\beta \to \infty$, i.e charged-AdS
black holes in the third order of the Lovelock gravity. Thus, it is shown that
the critical behaviors of these black holes are independent of the parameter
$\beta$ in the grand canonical ensemble.
