Holographic phase transition probed by non-local observables

From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordstr\"{o}m-AdS black hole is probed by the two point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes, the black hole undergos a Hawking-Page phase transition, a first order phase transition and a second order phase transition successively before it reaches to a stable phase. In addition, for these probes, we find the equal area law for the first order phase transition is valid always and the critical exponent of the heat capacity for the second order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.