Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state $T=T(v,P)$, we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the $T\ensuremath{-}v$ ($T\ensuremath{-}{r}_{h}$) line with fixed pressure $P$. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge $Q$ and dimension $d$. The result shows that the small/large black hole phase transitions appear for any $d$, which is reminiscent of the liquid/gas transition of a Van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for $d=6$ and $Q\ensuremath{\in}(0.1705,0.1946)$.

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