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 includes the cosmological constant $Lambda$ 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 rescaled temperature $tilde{T}$ in terms of other rescaled variables $ tilde{r}_{+}$, $tilde{q}$ and $tilde{h}$, where $r_{+}$ is the horizon radius, $q$ is the electric charge and $h$ is some magnetic parameter. For some values of $tilde{q}$ and $tilde{h}$, the phase structure of the black hole is uniquely determined. Moreover the peculiarity of multiple temperature with some fixed parameter configurations results in more rich phase structures. Focusing on the power Maxwell Lagrangian with $mathcal{L} left( sright) =s^{2}$, we obtain the corresponding phase diagrams in the $ tilde{q}$-$tilde{h}$ plane, then analyse the black holes phase structure and critical behaviour. For this case, the critical line is semi-infinite and extends to $tilde{h}=infty$. We also examine thermal stabilities of these black holes.