<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>P</mml:mi><mml:mtext>-</mml:mtext><mml:mi>v</mml:mi></mml:math> Criticality of a Specific Black Hole in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> Gravity Coupled with Yang-Mills Field

We study the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>P</mml:mi><mml:mtext>-</mml:mtext><mml:mi>v</mml:mi></mml:math> criticality of a specific charged AdS type black hole (SBH) in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> 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.

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