Eur. Phys. J. C (2015) 75: 559
https://doi.org/10.1140/epjc/s10052-015-3773-2

Regular Article - Theoretical Physics

Phase transitions in a holographic s  p model with back-reaction

¹ Kunming University of Science and Technology, Kunming, 650500, China
² State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O.Box 2735, Beijing, 100190, China
³ INPAC, Department of Physics, and Shanghai Key Laboratory of Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, 200240, China
⁴ Department of Physics, Robeson Hall, 0435, Virginia Tech, 850 West Campus Drive, Blacksburg, VA, 24061, USA
⁵ Department of Physics, Crete Center for Theoretical Physics, University of Crete, 71003, Heraklion, Greece

^* e-mail: phy_nzy@163.com
^** e-mail: niezy@itp.ac.cn

Received: 25 March 2015
Accepted: 5 November 2015
Published online: 27 November 2015

Abstract

In a previous paper (Nie et al. in JHEP 1311:087, arXiv:1309.2204 [hep-th], 2013), we presented a holographic s  p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction. The model shows a rich phase structure and various condensate behaviors such as the “n-type” and “u-type” ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s  p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s  p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back-reaction parameter, which show that the region for the s  p coexisting phase is enlarged with a small or medium back-reaction parameter but is reduced in the strong back-reaction cases.