$P-V$ criticality of a specific black hole in $f(R)$ gravity coupled with Yang-Mills field

We study the criticality of a specific charged AdS type black hole (SBH) in 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.