Holographic Van der Waals phase transition for a hairy black hole

The Van der Waals(VdW) phase transition in a hairy black hole is investigated by analogizing its charge, temperature, and entropy as the temperature, pressure, and volume in the fluid respectively. The two point correlation function(TCF), which is dual to the geodesic length, is employed to probe this phase transition. We find the phase structure in the temperature$-$geodesic length plane resembles as that in the temperature$-$thermal entropy plane besides the scale of the horizontal coordinate. In addition, we find the equal area law(EAL) for the first order phase transition and critical exponent of the heat capacity for the second order phase transition in the temperature$-$geodesic length plane are consistent with that in temperature$-$thermal entropy plane, which implies that the TCF is a good probe to probe the phase structure of the back hole.Comment: Accepted by Advances in High Energy Physics(The special issue: Applications of the Holographic Duality to Strongly Coupled Quantum Systems

Van der Waals phase transition in the framework of holography

Phase structure of the quintessence Reissner-Nordstr\"{o}m-AdS black hole is probed with the nonlocal observables such as holographic entanglement entropy and two point correlation function. Our result shows that, as the case of the thermal entropy, both the observables exhibit the similar Van der Waals-like phase transition. To reinforce the conclusion, we further check the equal area law for the first order phase transition and critical exponent of the heat capacity for the second order phase transition. We also discuss the effect of the state parameter on the phase structure of the nonlocal observables.Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.0038