Critical behaviors of a black hole in an asymptotically safe gravity with cosmological constant

We study the PV/r+ criticality and phase transition of a quantum-corrected black hole in asymptotic safety (AS) gravity in the extended phase space. For a black hole, the cosmological constant is dependent on the momentum cutoff or energy scale; therefore, one can naturally treat it as a variable and connect it with thermodynamic pressure. We find that for a quantum-corrected black hole there is a first-order phase transition similar to that of the van der Waals liquid-gas system. We also analyze the types of phase transition between the smaller and larger black hole phases according to Ehrenfestʼs classification. It is shown that they are second-order phase transitions.