Thermodynamic curvature in phase transitions for Hayward AdS black hole

We investigate $P$-$V$ criticality, with a focus on Ruppeiner geometry, in the extended phase space of Hayward anti-de Sitter (AdS) black holes. Through thermodynamic analysis, we confirm that Hayward-AdS black holes undergo distinct $P$-$V$ phase transitions and exhibit well-defined critical phenomena in the vicinity of their critical points. These behaviors are characterized by four critical exponents that typically obey the scaling laws predicted by mean-field theory–indicating a consistent thermodynamic framework with classical phase transition systems ($e\mathrm{.}g\mathrm{.},$ van der Waals fluids). Furthermore, we employ Ruppeiner geometry to probe the thermodynamic fluctuations of Hayward-AdS black holes, and by calculating the corresponding curvature scalar, we gain direct insights into the interaction nature of the black hole’s microscopic constituents.