Critical phenomena in the extended phase space of Kerr-Newman-AdS black holes

Treating the cosmological constant as a thermodynamic pressure, we investigate the critical behavior of a Kerr-Newman-AdS black hole system. The critical points for the van der Waals like phase transition are numerically solved. The highly accurate fitting formula for them is given and is found to be dependent of the charge $Q$ and angular momentum $J$. In the reduced parameter space, we find that the temperature, Gibbs free energy, and coexistence curve depend only on the dimensionless angular momentum-charge ratio $\epsilon=J/Q^2$ rather than $Q$ and $J$. Moreover, when varying $\epsilon$ from 0 to $\infty$, the coexistence curve will continuously change from that of the Reissner-Nordstr\"{o}m-AdS black hole to the Kerr-AdS black hole. These results may guide us to study the critical phenomena for other thermodynamic systems with two characteristic parameters.