Eur. Phys. J. C (2016) 76: 616
https://doi.org/10.1140/epjc/s10052-016-4463-4

Regular Article - Theoretical Physics

Phase structure of the Born–Infeld–anti-de Sitter black holes probed by non-local observables

¹ School of Material Science and Engineering, Chongqing Jiaotong University, Chongqing, 400074, China
² Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
³ Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
⁴ Center for Theoretical Physics, School of Sciences, Hubei University for Nationalities, Enshi, 445000, Hubei, China
⁵ State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, 100190, China

^* e-mail: xxzeng@itp.ac.cn

Received: 14 July 2016
Accepted: 25 October 2016
Published online: 9 November 2016

Abstract

With the non-local observables such as two point correlation function and holographic entanglement entropy, we probe the phase structure of the Born–Infeld–anti-de Sitter black holes. For the case , where b is the Born–Infeld parameter and Q is the charge of the black hole, the phase structure is found to be similar to that of the Van der Waals phase transition, namely the black hole undergoes a first order phase transition and a second order phase transition before it reaches a stable phase. While for the case , a new phase branch emerges besides the Van der Waals phase transition. For the first order phase transition, the equal area law is checked, and for the second order phase transition, the critical exponent of the heat capacity is obtained. All these results are found to be the same as that observed in the entropy–temperature plane.