Reentrant Hawking-Page phase transition of charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble

In this paper, we study the reentrant Hawking-Page transition in the grand canonical ensemble of Gauss-Bonnet AdS spacetime. We find that the four-dimensional Gauss-Bonnet hyperbolic AdS black hole always has a reentrant Hawking-Page transition in the range of electric potential 0<Phi<Phi(tr), accompanied by the appearance of the triple point. However, once the potential exceeds a certain upper limit Phi tr , i.e. Phi>Phi(tr), the Hawking-Page transition disappears. In the spacetime of five and higher dimensional Gauss-Bonnet hyperbolic AdS black hole, the reentrant Hawking-Page transition is solely observed to occur when the electric potential Phi lies between two specific thresholds (Phi(c)<Phi<Phi(tr). In scenarios where the electric potential is below Phi(c) (Phi<Phi(c)), only the standard Hawking-Page transition as in the the Einstein gravity is observed. Similar to the four-dimensional case, the Hawking-Page transition is negated when the electric potential exceeds Phi(tr) (Phi>Phi(tr)). We give the coexistence line, the triple point and critical point of the Hawking-Page transition in the phase diagram of the Gauss-Bonnet hyperbolic AdS black hole. The observed reentrant Hawking-Page transitions and triple points in the context of Gauss-Bonnet hyperbolic AdS black holes may correspond to the phase transitions and triple points in QCD phase diagrams, following the spirit of the AdS/CFT correspondence. To be a complete research, the Hawking-Page transition of d-dimensional charged spherical Gauss-Bonnet-AdS black hole in the grand canonical ensemble is also study in the Appendix, for which there exists a standard Hawking-Page transition with the transition temperature depending on the Gauss-Bonnet constant alpha.