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 for 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 where the central charge $C$ is a thermodynamic variable, we systematically explore both 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, marked by a characteristic swallowtail structure and coexistence curves with a negative slope. In contrast, within the mixed ensemble of 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 $\tilde{q}$: increasing $\tilde{q}$ lowers both the minimum and the Hawking-Page transition temperatures, significantly narrowing the stability window of the confined phase. These results, supported by detailed numerical analysis, reveal a rich, ensemble-dependent phase landscape and establish the non-linear Yang-Mills sector as a critical controller of confinement physics in strongly coupled holographic systems.