Phase transition and quantum corrections of quintessential Kerr-Newman black hole with cloud of strings

The purpose of this manuscript is to inspecting the phase transition and the critical phenomenon of charged quintessential Kerr-Newman-anti-de Sitter black hole with cloud of strings. In this regard, we evaluate the thermodynamic factors (Hawking temperature, angular momentum and entropy) in the framework of extended phase space. These factors fulfill the Smarr-Gibbs-Dehum equation in the existence of quintessence and cloud of strings. The critical behavior of thermodynamic factors is discussed via two techniques such as Maxwell equal-area law and Van-der Waal like equation of state. It is obtained that the former one is more effective to observe the critical nature of the complex black holes. Further, we study the phase diagram in T - S plane using equal-area law and obtain an isobar depicting the coexistence era of two phases. It is concluded that black holes lower than the critical temperature exhibit the phase transition same as that of Van-der Waal fluid. At the end, we analyze the influence of thermal variations on the black hole's stability.