QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes

Taking the quantum electrodynamics (QED) effect into account, we study the black hole phase transition and Ruppeiner geometry for the Euler-Heisenberg anti-de Sitter black hole in the extended phase space. For negative and small positive QED parameter, we observe a small/large black hole phase transition and reentrant phase transition, respectively. While a large positive value of the QED parameter ruins the phase transition. The phase diagrams for each case are explicitly exhibited. Then we construct the Ruppeiner geometry in the thermodynamic parameter space. Different features of the corresponding scalar curvature are shown for both the small/large black hole phase transition and reentrant phase transition cases. Of particular interest is that an additional region of positive scalar curvature indicating dominated repulsive interaction among black hole microstructure is present for the black hole with a small positive QED parameter. Furthermore, the universal critical phenomena are also observed for the scalar curvature of the Ruppeiner geometry. These results indicate that the QED parameter has a crucial influence on the black hole phase transition and microstructure.