Criticality of a Specific Black Hole in Gravity Coupled with Yang-Mills Field

We study the P-v criticality of a specific charged AdS type black hole (SBH) in f(R) gravity coupled with Yang-Mills field. In the extended phase space, we treat the cosmological constant as a thermodynamic pressure. After we study the various thermodynamical quantities, we show that the thermodynamic properties of the SBH behave as a Van der Waals liquid-gas system at the critical points and there is a first-order phase transition between small-large SBH.