Topology of dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

In this study, we employ the thermodynamic topological method to classify critical points for the dyonic AdS black holes with QTE in the EGB background. To this end, we find that there is a small/large BH phase transition in any space-time dimension, a conventional critical point exists with the total topological charge of Q_t=-1. The existence of the coupling constant α gives rise to a more intricate phase structure of the black hole, with the emergence of a triple points requires α≥0.5 and d=6. Interestingly, the condition for the simultaneous occurrence of small/intermediate and intermediate/large phase transition is that the coupling constant a takes a special value (α=0.5), the two conventional critical points (CP_1,CP_2) of the black hole are (physical) critical point, and the novel critical point that lacks the capability to minimize the Gibbs free energy. The critical point (Q_CP_1=Q_CP_2=-1) is observed to occur at the maximum extreme points of temperature in the isobaric curve, while the critical point (Q_CP_3=1), emerges at the minimum extreme points of temperature. Furthermore, the number of phases at the novel critical point exhibits an upward trend, followed by a subsequent decline at the conventional critical points. With the increase of the coupling constant (α = 1 ), although the system has three critical points, only CP_1 is a (physical) critical point, and the CP_2 serves as the phase annihilation point. This means that the coupling constant α has a non-negligible effect on the phase structure of the black hole.