Phase transitions in a holographic s [Formula: see text] p model with back-reaction

In a previous paper (Nie et al. in JHEP 1311:087, arXiv:1309.2204 [hep-th], 2013), we presented a holographic s [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] p coexisting phase is enlarged with a small or medium back-reaction parameter but is reduced in the strong back-reaction cases.