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-v (T-r₇) 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 (0. 1705, 0. 1946).