Thermodynamics and phase transition of anti de Sitter black holes with ModMax nonlinear electrodynamics and perfect fluid dark matter

Abstract In this paper, we investigate the thermodynamics and phase transitions of asymptotically anti-de Sitter black holes (BHs) in the presence of ModMax nonlinear electrodynamics (NLED) and perfect fluid dark matter (PFDM). Combining the effects of ModMax theory, characterized by the nonlinearity parameter $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> , and PFDM, described by the parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , we derive an exact solution for the BH metric and analyze its thermodynamic properties. We explore the critical behavior of the BHs by studying the Hawking temperature, heat capacity, and Gibbs free energy. The results demonstrate the existence of phase transitions analogous to those found in van der Waals fluids, with the ModMax parameter and dark matter playing crucial roles in modifying the critical points and stability of the BH. In addition, we employ geometric thermodynamic methods (GTM), including the Weinhold, Ruppeiner, and HPEM metrics, to further examine the stability and phase structure of BHs. Our study provides new insights into how NLED and dark matter are interrelated within BH thermodynamics.