arXiv subjects

Zi-Qiang Zhao

Publications and source records attributed to Zi-Qiang Zhao.

15 recordsLinked to original sources

arXiv2026

Universal fingerprint of topological defect cores

Topological defects are ubiquitous in physics, arising from condensed matter physics to the early universe. Although there exist many universal scaling laws for correlations between topological defects, such as Porod scaling, the fingerprint of topological defect cores has remained largely unexplored. Here, we discover a universal scaling law in the region $k>1/ξ$, where $ξ$ is the healing length of the topological defects, taking the scaling of the form factor $S_f \propto k^{-(d+p+2)}$, where $d$ is the spatial dimension and $p$ is the defect codimension. We analytically prove that this exponent originates from a universal V-shaped cusp at the defect core and is independent of the underlying system and dynamics. Numerical simulations verify this scaling law in four typical frameworks: the time-dependent Ginzburg-Landau and Gross-Pitaevskii equations in the weak-coupling regime, the gauge/gravity duality model in the strong-coupling regime, and the Klein-Gordon equation in the Friedmann-Robertson-Walker background in cosmology. Our work provides a new probe for studying topological defects in systems ranging from superconductors to cosmological phase transitions.

hep-th↗

arXiv2026

Interior geometry of black holes as a probe of first-order phase transition

Traditional diagnostics of black hole phase transitions rely on thermodynamic quantities defined at the event horizon or asymptotic boundary. Here, we demonstrate that the near-singularity geometry offers a sharp, independent probe of both first-order phase transitions and supercritical crossover. For scalarized AdS black holes exhibiting a first-order phase transition, the Kasner exponent $p_t$, which characterizes the approach to the singularity, undergoes a dramatic transformation. On one side of the transition, $p_t$ oscillates strongly with temperature, reflecting violent interior dynamics. On the other side, it becomes a smooth, monotonically varying function. These two distinct behaviors converge as the critical point is approached. Beyond the critical point, in the supercritical region, $p_t(T)$ develops a distinct extremum, defining a Kasner crossover line that is entirely independent of traditional thermodynamic (Widom line) or dynamic (Frenkel line) criteria. Our work establishes the near geometry of singularity of scalarized black hole as a novel class of diagnostics for phase transitions, revealing that a change in the macroscopic thermodynamic state fundamentally reshapes the deepest interior structure of spacetime.

gr-qc↗

arXiv2026

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions

First-order phase transitions of black holes have been extensively studied within thermodynamic frameworks, yet the corresponding evolution of spacetime geometric properties remains unclear. This paper establishes a purely differential geometric framework to probe such phase transitions by analyzing the curvature of unstable null orbits. Using the geodesic curvature of the null circular orbit in the optical metric to locate the light ring, we demonstrate that the corresponding Gaussian curvature $K$ serves as a direct geometric signature of the phase transition. During a first-order phase transition, the curve $K$ versus temperature $T$ exhibits a multivalued structure within the spinodal region, precisely mirroring the swallowtail behavior of the free energy. Numerical analysis of Hayward-Letelier-AdS black holes confirms the effectiveness of this geometric signature. Our work demonstrates that the intrinsic geometric quantities of spacetime encode the information of black hole phase transitions. These quantities serve as geometric probes of black hole phase transitions, while their discontinuity between the small and large black hole branches exhibits order parameter-like behavior. As an extension of this geometric probe, we also find that the Gaussian curvature exhibits a heat-capacity-like divergence at the second-order phase transition point. These results provide a purely geometric foundation for understanding the correspondence between thermodynamics and spacetime curvature in the null case.

gr-qc↗

arXiv2026

Nonequilibrium crossover in the supercritical region from quench dynamics

Distinguishing different subphases in the supercritical region is an important issue in statistical physics and condensed matter physics. Traditional approaches rely mainly on static thermodynamic response functions or equilibrium correlation functions, which are essentially limited to quasistatic processes. In this paper, we investigate the evolution behavior of a system after a rapid quench from the perspective of nonequilibrium dynamics within a holographic model. We find that, using the time at which inhomogeneous structures appear most rapidly, we can define a supercritical crossover curve based on the pure phase separation process. In addition, the uniform invasion phenomenon induced by topological defects persists in the supercritical region, and the invasion velocity exhibits a clear turning point as a function of the quench endpoint. This turning point can define another new nonequilibrium supercritical crossover line that simultaneously incorporates the effects of both symmetry breaking and phase separation. Unlike the classical Widom line or Frenkel line, these two new crossover lines contain both thermodynamic information and dynamical information, reflecting the dynamical nature of the supercritical region under nonequilibrium conditions. This work provides a novel nonequilibrium dynamical approach for characterizing supercritical subphases.

cond-mat.stat-mech↗

arXiv2026

Phase transitions in scalarized topological AdS black holes

We investigate the behavior of black hole scalarization induced by a charged scalar field in the extended phase space of the asymptotic AdS spacetime with three distinct horizon topologies. The results indicate that in all three cases, the charged black hole spacetime undergoes scalarization at low temperatures. Notably, the spherical topology is unique in that its domain of scalarization theoretically extends to much higher temperatures under low pressure in the extended phase space. Moreover, the scalarization process in the spherical case exhibits complex phase transition behaviors without additional non-linear terms, which are similar to those in the planar and hyperbolic topologies with the assistance of non-linear terms. With increasing pressure in the extended phase space, the condensate of the scalarization in all three cases undergoes a transition from the first-order style to a cave-of-wind style. This study provides deeper insight into the zeroth-order phase transition during black hole scalarization and reveals the complete phase structure of black holes in the extended phase space.

gr-qc↗

arXiv2026

Phase separation seeded by Z2 and U(1) topological defects from holography

We study the interaction between spontaneous symmetry breaking and phase separation dynamics in holography. Using a double-quench protocol, the system first rapidly crosses the critical point and generates topological defects, while a second quench drives the system into a nonlinear unstable regime with spinodal decomposition. We investigate both $\mathbb{Z}_2$ and $U(1)$ symmetric systems, where different types of topological defects emerge during symmetry breaking. We show that topological defects dynamically determine the nucleation sites of phase separation. As the instability grows, the defect cores expand into macroscopic phase-separated domains. Despite the distinct symmetries and topological properties of these defects, both systems exhibit the same universal dynamical behavior, indicating that topological defects can universally serve as dynamical seeds for subsequent phase separation.

hep-th↗

arXiv2026

Topological defect induced phase separation in a holographic system

We investigate the coupled dynamics of symmetry breaking and phase separation during quenches across the critical point in a first-order phase transition. Based on the Einstein-Maxwell-scalar theory, we construct a holographic superfluid model with $\mathbb{Z}_2$ symmetry. By introducing higher-order nonlinear terms $λΨ^4$ and $τΨ^6$ into the scalar field potential, we realize a rich phase structure, which enables us to study the coupling effects between symmetry breaking and phase separation. Furthermore, by preparing initial conditions with well-defined spatial partitions, we discover a new triggering mechanism for the invasion phenomenon, namely that kinks serve as triggering sites for the phase separation process. This study reveals a novel coupling mechanism between topological defects and phase separation, enriches our understanding of nonequilibrium structure formation in strongly coupled systems.

hep-th↗

arXiv2026

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 $λ|ψ|^4$, $τ|ψ|^6$, 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.

gr-qc↗

arXiv2026

Interior structure of black holes with nonlinear terms

We investigate the oscillation of the Kasner exponent $p_t$ near critical point of the hairy black holes dual to holographic superfluid and reveal a clear inverse periodicity $f(T_c/(T_c-T))$ in a large region below the critical temperature. We first introduce the fourth-power term with a coefficient $λ$ to adjust the oscillatory behavior of the Kasner exponent $p_t$ near the critical point. Importantly, we show that the nonlinear coefficient $λ$ provides accurate control of this periodicity: a positive $λ$ stretches the region, while a negative $λ$ compresses it. By contrast, the influence of another coefficient $τ$ is more concentrated in regions away from the critical point. This work provides a new perspective for understanding the complex dynamical structure inside black holes and extends the actively control from the fourth- and sixth-power term into the black hole interior region.

gr-qc↗

arXiv2025

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 $λ$ and $τ$. 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 $λ-τ$ parameter space that characterizes different transition types. For a slightly negative $λ$, we further establish a $τ-ρ$ 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 $λ$ and $τ$. The comprehensive phase diagrams and quantitative transition criteria we provide offer a valuable resource for future studies.

hep-th↗

arXiv2025

Characterized behaviors of black hole thermodynamics in the supercritical region

The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure. This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region. By making use of the free energy, we introduce three key thermodynamic quantities: scaled variance, skewness, and kurtosis. Our results demonstrate that the Widom line, associated with the maximal scaled variance, can effectively differentiate between small and large black hole-like subphases, each displaying distinct thermodynamic behaviors within the supercritical region. Furthermore, by utilizing quasinormal modes, we identify the Frenkel line, offering a dynamic perspective to distinguish between small and large black hole-like subphases. These contribute to a deeper comprehension of black hole subphases in the supercritical region, thus illuminating new facets of black hole thermodynamics.

gr-qc↗

arXiv2025

Phase transitions in a holographic superfluid model with non-linear terms beyond the probe limit

We study the holographic s-wave superfluid model with 4th and 6th power self-interaction terms $λ|ψ|^4$ and $τ|ψ|^6$ with considering the full back-reaction of the matter fields on the metric in the 3+1 dimensional bulk. The self-interaction terms are good at controlling the condensate to realize various phase transitions, such as the zeroth-order, first-order, and second-order phase transitions within the single condensate s-wave superfluid model. Therefore, in this work, we are able to investigate the influence of the back-reaction strength on the various phase transitions, including the zeroth and first order phase transitions. In addition, we confirm that the influence of the 4th and 6th power terms on the superfluid phase transition in the case of finite back-reaction are qualitative the same as in the probe limit, thus present universality. We also plot the special value $λ_s$ of the parameter $λ$ at different back-reaction strength, below which the condensate grows to an opposite direction and is important in controlling the order of the superfluid phase transitions. Comparing the influence of the back-reaction parameter and that of the higher-order nonlinear coefficients, we see that the back-reaction strength brings in both the effective couplings similar to the 4th power and 6th power terms.

hep-ph↗

arXiv2024

Dynamical evolution of spinodal decomposition in holographic superfluids

We study the nonlinear dynamical evolution of spinodal decomposition in a first-order superfluid phase transition using a simple holographic model in the probe limit. We first confirm the linear stability analysis based on quasinormal modes and verify the existence of a critical length scale related to a gradient instability -- negative speed of sound squared -- of the superfluid sound mode, which is a consequence of a negative thermodynamic charge susceptibility. We present a comparison between our case and the standard Cahn-Hilliard equation for spinodal instability, in which a critical length scale can be also derived based on a diffusive instability. We then perform several numerical tests which include the nonlinear time evolution directly from an unstable state and fast quenches from a stable to an unstable state in the spinodal region. Our numerical results provide a real time description of spinodal decomposition and phase separation in one and two spatial dimensions. We reveal the existence of four different stages in the dynamical evolution, and characterize their main properties. Finally, we investigate the strength of dynamical heterogeneity using the spatial variance of the local chemical potential and we correlate the latter to other features of the dynamical evolution.

hep-th↗

arXiv2024

Dynamical and thermodynamic crossovers in the supercritical region of a holographic superfluid model

Many physical systems, including classical fluids, present in their phase diagram the competition between two phases that are separated by a line of first-order phase transitions which terminates at a so-called critical point. Despite several proposals, in the supercritical region beyond the critical point, whether the two phases can still be distinguished and by which criterion remain open questions. In this work, we study the thermodynamics and linear dynamics of a holographic superfluid model with nonlinear potential terms in the supercritical region. We identify the presence of a dynamical crossover, akin to the liquid-like to gas-like Frenkel transition in supercritical fluids, and we define other separation lines of thermodynamic origin based on higher order derivatives of the free energy with respect to the charge density. Our results highlight the universal dynamical and thermodynamic features of supercritical systems from nuclear matter and classical fluids to superfluid systems.

hep-th↗

arXiv2023

Dynamical stability from quasi normal modes in 2nd, 1st and 0th order holographic superfluid phase transitions

We study a simple extension of the original Hartnoll, Herzog and Horowitz (HHH) holographic superfluid model with two nonlinear scalar self-interaction terms $λ|ψ|^4$ and $τ|ψ|^6$ in the probe limit. Depending on the value of $λ$ and $τ$, this setup allows us to realize a large spectrum of holographic phase transitions which are 2nd, 1st and 0th order as well as the ``cave of wind'' phase transition. We speculate the landscape pictures and explore the near equilibrium dynamics of the lowest quasinormal modes (QNMs) across the whole phase diagram at both zero and finite wave-vector. We find that the zero wave-vector results of QNMs correctly present the stability of the system under homogeneous perturbations and perfectly agree with the landscape analysis of homogeneous configurations in canonical ensemble. The zero wave-vector results also show that a 0th order phase transition cannot occur since it always corresponds to a global instability of the whole system. The finite wave-vector results show that under inhomogeneous perturbations, the unstable region is larger than that under only homogeneous perturbations, and the new boundary of instability match with the turning point of condensate curve in grand canonical ensemble, indicating a new explanation from the subsystem point of view. The additional unstable section also perfectly match the section with negative value of charge susceptibility.

hep-th↗