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Advances in High Energy Physics
Volume 2017, Article ID 2356174, 8 pages
Research Article

Holographic van der Waals Phase Transition for a Hairy Black Hole

1School of Material Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China
2State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
3School of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing 400070, China

Correspondence should be addressed to Xiao-Xiong Zeng; moc.361@scisyhpgnezxx

Received 2 March 2017; Accepted 29 May 2017; Published 12 July 2017

Academic Editor: Bum-Hoon Lee

Copyright © 2017 Xiao-Xiong Zeng and Yi-Wen Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


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-thermal entropy plane besides the scale of the horizontal coordinate (geodesic length plane resembles that in the temperature). 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-thermal entropy plane (geodesic length plane is consistent with that in temperature), which implies that the TCF is a good probe to probe the phase structure of the back hole.