Stability analysis and double critical phenomenon in the Einstein-Maxwell-scalar theory

We investigate the dynamical stability and phase transition behavior in a holographic superfluid model incorporating higher-order self-interaction terms $\lambda |\psi|^4$, $\tau|\psi|^6$, and a non-minimal coupling $h(\psi)=e^{\alpha|\psi|^2}$. Thermodynamic and dynamical stability analyzes show that the thermodynamic stability and dynamical stability of the system are consistent. Phase diagram analysis reveals rich critical and supercritical phenomena. For fixed $\lambda<0$ and $\alpha$, increasing $\tau$ shrinks the first-order phase transition region to a critical point and then enters the supercritical region. When varying $\alpha$, the system can exhibit no critical point and, most notably, a double critical phenomenon in which, as $\alpha$ increases, the system first enters the supercritical region and then re-enters the first-order phase transition region. This double critical phenomenon driven by a single parameter is reported for the first time in holographic superfluid models, revealing a complex nonmonotonic coupling effect between the non-minimal coupling and higher-order interaction terms.