Extended phase space thermodynamics of regular-AdS black hole

After obtaining an exact regular-AdS black hole resulting from the coupling of general relativity with nonlinear electrodynamics (NED), we explore the thermodynamics of the extended phase space, treating the cosmological constant ( $$ ) as the pressure (P) of the black holes and its conjugate as thermodynamic volume (V). Considering the NED parameter (g), we investigate the Hawking temperature, entropy, Gibb's free energy and specific heat at the horizon radius. Due to the presence of NED charge, the black hole exhibits van der Waals-like phase transition instead of Hawking-Page phase transition, which could be observed through the $$ plots, which display a swallowtail pattern below the critical pressure, and it gives rise to second-order phase transitions when pressure attains its critical value. The first-order phase transition shares similarities with the liquid-gas phase transition. We determine the exact critical points and explore the influence of NED on $$ criticality, revealing that the isotherms undergo a liquid-gas-like phase transition for temperatures below its critical value $$ , especially at lower $$ . The identical critical exponent to that of the van der Waals fluid suggests that the NED does not alter the critical exponents, as observed in other arbitrary AdS black holes.