Holographic phase transition probed by non-local observables

TL;DR

This paper investigates the phase transitions of a 5D Reissner-Nordström-AdS black hole using holographic non-local observables, revealing consistent phase behavior and critical exponents across different probes.

Contribution

It demonstrates that holographic non-local observables can effectively probe the phase structure and critical phenomena of black holes, confirming the validity of the equal area law and mean field critical exponents.

Findings

Black hole undergoes successive phase transitions: Hawking-Page, first order, second order.

Equal area law holds for the first order phase transition.

Critical exponent matches mean field theory, independent of boundary region size.

Abstract

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.