Various phase transitions in a holographic p-wave superfluid model with nonlinear terms

This study investigates various phase transitions, including those of 2nd, 1st, and 0th order, in a holographic p-wave superfluid model incorporating 4th- and 6th-order nonlinear terms with coefficients $\lambda$ and $\tau$. We demonstrate that these nonlinear terms provide universal control over the phase transitions of the p-wave model, qualitatively consistent with findings in the holographic s-wave case. By analyzing the condensate and free energy behavior across typical phase transitions, we quantitatively map out the $\lambda-\tau$ parameter space that characterizes different transition types. For a slightly negative $\lambda$, we further establish a $\tau-\rho$ phase diagram featuring a line of first-order phase transition points that terminates at a critical point, beyond which lies a supercritical region. Our results confirm the precise tunability of the p-wave superfluid phase transitions through $\lambda$ and $\tau$. The comprehensive phase diagrams and quantitative transition criteria we provide offer a valuable resource for future studies.