Thermodynamics and phase transition of Bardeen-AdS-class black holes

In a generalized parameter space, regular black holes can be regarded as non-singular solutions under specific parameters in Einstein gravity theory coupled with non-linear electromagnetic fields. Following this concept, we investigate the thermodynamic states and phase transitions of Bardeen-AdS-class black holes, revealing that the system can be classified into two categories, Type I and Type II, based on whether it adopts a pure Bardeen-AdS spacetime without event horizons or a Bardeen-AdS black hole as its phase state, each exhibiting distinct thermodynamic properties. If one includes the Bardeen-AdS black holes in the system (Type I), there will be three distinct black hole states and the phase transitions between them are analogous to the Reissner-Nordstrom-AdS black holes. On the other hand, if the pure Bardeen-AdS spacetime is included (Type II), an additional tiny black hole state emerges. A phase transition reminiscent of the Hawking-Page transition was found. Significantly, in this scenario, thermodynamical characteristic curves exhibit discontinuous behavior, which attributes to the multiple horizons. The presence of a Bardeen-AdS black hole within the phase structure of the Bardeen-AdS-class black hole profoundly modifies the thermodynamical properties of the system, highlighting the novel aspects of regular black holes.