Extended phase space thermodynamics for dyonic black holes with a power Maxwell field

In this paper, we investigate the thermodynamics of dyonic black holes with the presence of power Maxwell electromagnetic field in the extended phase space, which regards the cosmological constant A as a thermodynamic variable. For a generic power Maxwell black hole with the electric charge and magnetic charge, the equation of state is given as the function of resealed temperature (T) over tilde in terms of other resealed variables (r) over tilde (+), (q) over tilde, and (h) over tilde, where r(+) is the horizon radius, q is the electric charge, and h is the magnetic parameter. For some values of (q) over tilde and (h) over tilde, the phase structure of the black hole is uniquely determined. Moreover, the peculiarity of multiple temperature with some parameter configurations results in complex phase structures. Focusing on the power Maxwell Lagrangian with L(s) = s(2), we obtain the corresponding phase diagrams in the (h) over tilde-(q) over tilde plane where the critical line extends to (h) over tilde = + infinity. Then, we analyze the black holes' phase structure and critical behavior and display phase transition curves with different (h) over tilde in the (q) over tilde-(T) over tilde plane. We also examine thermal stabilities of these black holes.