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

Abstract

We investigate the dynamical stability and phase transition behavior in a holographic superfluid model incorporating higher-order self-interaction terms $λ|ψ|^4$, $τ|ψ|^6$, and a non-minimal coupling $h(ψ)=e^{α|ψ|^2}$. 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 $λ<0$ and $α$, increasing $τ$ shrinks the first-order phase transition region to a critical point and then enters the supercritical region. When varying $α$, the system can exhibit no critical point and, most notably, a double critical phenomenon in which, as $α$ 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.

Figures (11)

• Figure 1: The condensate and free energy for $\lambda=0$ and $\tau=0$ with $\alpha=5$. The dashed lines correspond to the normal solution, and the solid lines correspond to the superfluid solution.
• Figure 2: The quasinormal modes for $\lambda=0$ and $\tau=0$ with $\alpha=5$. In which different shapes and colors denote modes of different orders.
• Figure 3: The condensate and free energy for $\lambda=-4$ and $\tau=0$ with $\alpha=5$. The dashed lines correspond to the normal solution, and the solid lines correspond to the superfluid solution.
• Figure 4: The quasinormal modes for $\lambda=-4$ and $\tau=0$ with $\alpha=5$. In which different colors correspond to different solutions in Fig. \ref{['c0th']}. The modes shown here are all purely imaginary modes.
• Figure 5: The condensate and free energy for $\lambda=-4$ and $\tau=2.68$ with $\alpha=5$. The dashed lines correspond to the normal solution, and the solid lines correspond to the superfluid solution.