Thermodynamics and phase transition in central charge criticality of charged Gauss-Bonnet AdS black holes

In this paper, we investigate the thermodynamics of D-dimensional charged Gauss-Bonnet black holes in anti-de Sitter spacetime. Varying the cosmological constant, Newton constant and Gauss-Bonnet coupling constant in the bulk, one can rewrite the first law of thermodynamics for black holes. Furthermore, we introduce the central charge and study the critical behaviors, which show the apparent discrepancy from other black holes. Based on this approach, we disclose the phase transition structures in $D=4,5$, and $6$. Besides, a triple point where the small/intermediate/large black holes can coexist is found in $D=6$.