Dark-Sector Effects on the Phase Structure of Nonlinear Magnetic AdS Black Holes

We investigate the effects of perfect fluid dark matter (PFDM) and a dark-energy field on the phase structure of a nonlinear magnetically charged Anti–de Sitter (AdS) black hole. We find that the small–large black hole (SBH/LBH) phase transition is driven by the nonlinear magnetic sector, while the dark sector does not generate additional transitions. In particular, increasing the magnitude of the PFDM parameter $\lambda$ suppresses this phase transition, eventually driving the system toward a single-phase regime. Moreover, a nonzero $\lambda$ prevents the formation of a regular black hole core. The effect of the dark-energy field depends on its equation-of-state parameter: in the quintessence regime, increasing its intensity strengthens the first-order phase transition, increasing the Gibbs construction area and latent heat while reducing the critical regime; in the phantom regime, the system exhibits spinodal behavior without phase coexistence. Finally, geometrothermodynamics (GTD) shows that the curvature singularities of the thermodynamic equilibrium manifold reproduce the phase structure of the black hole, while the associated power-law scaling near criticality is consistent with previous results for black holes, cosmological horizons, and real fluids, suggesting a universal thermodynamic behavior across these systems.