Microstructure and continuous phase transition of a Reissner-Nordstrom-AdS black hole

It is well known that a Reissner-Nordstrom-AdS (RN-Ads) black hole has a phase transition which is similar to that of the van der Waals system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On this basis, we introduce a new order parameter and use the Landau continuous phase transition theory to discuss the critical phenomenon of the RN-AdS black hole and give the critical exponent. By constructing the binary fluid model of black hole molecules, we investigate the microstructure of black holes. Furthermore, by studying the effect of the spacetime scalar curvature on the phase transition, we find that the charged and uncharged molecules of black holes are with different microstructures such as fermion gas and boson gas.