T $T$ – S $S$ criticality of black holes with power Maxwell invariant source

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In this paper, we show that black holes with PMI source exhibit the $T$ – $S$ criticality and derive the relevant critical physical quantities analytically. The values of critical quantities for the case $s\neq1$ vary from those for the case $s=1$ , showing the effect of PMI field on the critical phenomena of black holes. When $q< q_{c}$ , the $T$ – $S$ curve can be divided into three branches by a maximum point and a minimum point of Hawking temperature. With the help of specific heat analysis, we further show that the small entropy branch and the large entropy branch are stable. However, the medium entropy branch is unstable and can be removed via the technique of free energy analysis. Moreover, we examine the Maxwell equal area law and find that the relative errors for all the cases are small enough. So the existence of the PMI field does not affect the Maxwell equal area law.