Davies-type phase transitions in 4D Dyonic AdS black holes from topological perspective

In this work, we discussed the Davies-type phase transitions in two distinct categories of dyonic AdS black holes (BHs). The first one is dyonic AdS BHs within four-dimensional spacetime framework. The second one is the dyonic BHs with quasitopological electromagnetism (QE) in Einstein-Gauss-Bonnet gravity (EGBG). First, we analyze the increasing and decreasing behavior of divergency depending upon different parameters which provides useful information about the region that are physical and stable. We also discuss the critical behavior of BHs in three different statistical ensembles: the canonical, mixed and grand canonical. It is noted that BHs can be classified into distinct topological classes based on their topological charge ($Q$) which assumes discrete values of $0,+1,-1$. This topological charge plays a pivotal role in determining the phase structure and stability of the BHs within each ensemble. A topological charge of 0 corresponds to a neutral topological state that could be indicative of a more complex underlying structure, while charges of +1 or −1 indicate the presence of additional structures such as magnetic monopoles or dyons, which significantly influence the thermodynamic properties and phase transitions of the system.