Abstract
From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-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 that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that 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.
Highlights
Phase transition is a ubiquitous phenomenon for gardenvariety thermodynamic systems
It has been shown that a charged AdS black hole undergoes a Hawking-Page phase transition [6, 7], which is interpreted as the confinement/deconfinement phase transition in the dual gauge field theory [8] and a van der Waals-like phase transition before it reaches the stable state [9]
In the extended phase space, where the negative cosmological constant is treated as the pressure while its conjugate acts as the thermodynamical volume, the van der Waals-like phase transition has been observed in the P-V plane [10,11,12,13,14,15,16]
Summary
Phase transition is a ubiquitous phenomenon for gardenvariety thermodynamic systems. Due to the pioneering work by Hawking [1, 2], a black hole is a thermodynamic system. We intend to probe the Hawking-Page phase transition and van der Waals-like phase transition appeared in a 5-dimensional Reissner-Nordstrom-AdS black hole by the geodesic length, minimal area surface, and minimal surface area in the bulk, which are dual to the nonlocal observables on the boundary theory by holography, namely, the twopoint correlation function, Wilson loop, and entanglement. Very recently [29] investigated entanglement entropy for a quantum system with infinite volume; their result showed that the entanglement entropy exhibits the same van der Waals-like phase transition as the thermal entropy They checked the equal area law and obtained the critical exponent of the heat capacity near the critical point. It is noteworthy that by holography the whole phase structure described above is for the bulk black hole and for the dual boundary system, where the thermal entropy is given by the black hole entropy, and so on
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