Holographic multi-condensate with nonlinear terms

We study the influence of nonlinear terms quartic of the charged fields, which do not change the critical points of single condensate solutions, on the phase structure of a holographic model with multi-condensate in probe limit. We include one s-wave order and one p-wave order charged under the same U(1) gauge field in the holographic model and study the influence of the three quartic nonlinear terms of the charged fields with coefficients $\lambda_s$, $\lambda_p$ and $\lambda_{sp}$ on the phase structure. We show the influence of each of the three parameters on the phase diagram with other two set to zero, respectively. With these nonlinear terms, we get more power on tuning the phase structure of the holographic system showing multi-condensate, and show how to get a reentrant phase transition as an example.