Holographic CFT phase transitions and criticality for Einstein–Maxwell–Power–Yang–Mills AdS black holes

We present a comprehensive study of the thermodynamic phase structure of Anti-de Sitter black holes in Einstein–Maxwell–Power–Yang–Mills gravity, reformulated through holographic duality as an ensemble problem in the dual conformal field theory (CFT). By deriving an extended first law in which the central charge C is treated as a thermodynamic variable, we systematically explore both the canonical and mixed ensembles. In the canonical ensemble with fixed charges, we identify a van der Waals-like phase transition between small and large black holes, characterized by a swallowtail structure and coexistence curves with a negative slope. In contrast, within the mixed ensemble at fixed electric potential, the system exhibits a Hawking–Page transition between confined and deconfined phases of the boundary CFT. Our key finding is the suppressive role of the non-Abelian Yang–Mills charge q̃ q ~ : increasing q̃ q ~ lowers both the minimum temperature and the Hawking–Page transition temperature, thereby significantly narrowing the stability window of the confined phase. Supported by detailed numerical analysis, these results reveal a rich, ensemble-dependent phase landscape and establish the nonlinear Yang–Mills sector as a critical controller of confinement physics in strongly coupled holographic systems.