Zeroth Order Phase Transition Research Articles

Lagrangian Partition Functions Subject to a Fixed Spatial Volume Constraint in the Lovelock Theory.

We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory. Those stationary points take exactly the same forms as in Einstein gravity. The logarithm of Z corresponding to a zero effective cosmological constant indicates that the Bekenstein-Hawking entropy of the boundary area and that corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also show the existence of zeroth-order phase transitions between different vacua, a phenomenon distinct from Einstein gravity.

Solutions and basic properties of regularized Maxwell theory

The regularized Maxwell theory is a recently discovered theory of nonlinear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique nonlinear electrodynamics (that depends only on the field invariant ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$) whose radiative solutions can be found in the Robinson-Trautman class. At the same time, it is the only electrodynamics of this type (apart from Maxwell) whose slowly rotating solutions are fully characterized by the electrostatic potential. In this paper, after discussing the basic properties of the regularized Maxwell theory, we concentrate on its spherical electric solutions. These not only provide ``the simplest'' regularization of point electric field and its self-energy, but also feature complex thermodynamic behavior (in both canonical and grand canonical ensembles) and admit an unprecedented phase diagram with multiple first-order, second-order, and zeroth-order phase transitions. Among other notable solutions, we construct a novel C-metric describing accelerated AdS black holes in the regularized Maxwell theory. We also present a generalization of the regularized Maxwell Lagrangian applicable to magnetic solutions, and find the corresponding spherical, slowly rotating, and weakly Newman-Unti-Tamburino charged solutions.

The mixed-state entanglement in holographic p-wave superconductor model

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

AdS/BCFT and Island for curvature-squared gravity

In this paper, we investigate AdS/BCFT for curvature-squared gravity. To warm up, we start with Gauss-Bonnet gravity. We derive the one point function of stress tensor and show that the central charge related to the norm of displacement operator is positive for the couplings obeying causality constraints. Furthermore, by imposing the null energy condition on the end-of-the-world brane, we prove the holographic g-theorem for Gauss-Bonnet gravity. This corrects a wrong point of view in the literature, which claims that the holographic g-theorem is violated for Gauss-Bonnet gravity. As a by-product, we obtain the boundary entropy and A-type boundary central charges in general dimensions. We also study AdS/BCFT for general curvature-squared gravity. We find that it is too restrictive for the shape of the brane and the dual BCFT is trivial if one imposes Neumann boundary conditions for all of the gravitational modes. Instead, we propose to impose Dirichlet boundary condition for the massive graviton, while imposing Neumann boundary condition for the massless graviton. In this way, we obtain non-trivial shape dependence of stress tensor and well-defined central charges. In particular, the holographic g-theorem is satisfied by general curvature-squared gravity. Finally, we discuss the island and show that the Page curve can be recovered for Gauss-Bonnet gravity. Interestingly, there are zeroth-order phase transitions for the Page curve within one range of couplings obeying causality constraints. Generalizing the discussions to holographic entanglement entropy and holographic complexity in AdS/CFT, we get new constraints for the Gauss-Bonnet coupling, which is stronger than the causality constraint.

Holographic CFT phase transitions and criticality for charged AdS black holes

We study the holographic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton’s constant. In the dual CFT this corresponds to including the central charge C and its chemical potential μ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy (T, S), electric potential vs. charge ( overset{sim }{Phi},overset{sim }{Q} ) and field theory pressure vs. volume (p, mathcal{V} ). For the (grand) canonical ensembles at fixed ( overset{sim }{Q},mathcal{V},C ), ( overset{sim }{Phi},mathcal{V},C ) and ( overset{sim }{Q},mathcal{V},mu ), based on the holographic dictionary, we argue the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed ( overset{sim }{Q},mathcal{V},mu ) we find a new zeroth-order phase transition between a high- and low-entropy phase at some μ-dependent temperature. Finally, we point out there is no critical behaviour in the fixed p ensembles, i.e. there is no p − mathcal{V} criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid. Whether or not this phase structure is supported by CFT computations remains an interesting open question.

Higher-derivative holography with a chemical potential

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Phase transitions in 4D Gauss–Bonnet–de Sitter black holes

We investigate thermodynamic aspects of black holes in the recently formulated four dimensional Gauss-Bonnet theory of gravity, focusing on its asymptotically de Sitter ($\Lambda>0$) solutions. We take a Euclidean path integral approach, where thermodynamic data is fixed at a finite radius `cavity' outside the black hole to achieve equilibrium in the presence of the cosmological horizon. Working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure, we study the phase structure of both uncharged and charged solutions, uncovering a wealth of phenomena. In the uncharged case, black holes are found to undergo either the standard Hawking-Page-like transition to empty de Sitter space or a small-large transition (akin to those seen in charged AdS black holes in pure Einstein gravity) depending on the pressure. We also find a triple point where the radiation, small, and large black hole phases coexist, and a zeroth-order phase transition within a narrow range of Gauss-Bonnet coupling parameter. Reentrant phase transitions between radiation and a small black hole also exist inside a certain parameter range. Similar phenomena are found in the charged case, with the charge parameter playing a role analogous to the Gauss-Bonnet coupling parameter in determining the phase structure.

Scalarized Einstein\u2013Maxwell-scalar black holes in a cavity

In this paper, we study the spontaneous scalarization of Reissner–Nordström (RN) black holes enclosed by a cavity in an Einstein–Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions are always thermodynamically preferred over RN black holes in a cavity. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge Q.

Scalarized Einstein\u2013Maxwell-scalar black holes in anti-de Sitter spacetime

In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in an Einstein–Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner–Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a micro-canonical ensemble, scalarized solutions are always thermodynamically preferred over RNAdS black holes. However, the system has much richer phase structure and phase transitions in a canonical ensemble. In particular, we report a RNAdS BH/scalarized BH/RNAdS BH reentrant phase transition, which is composed of a zeroth-order phase transition and a second-order one.

Effective thermodynamical system of Schwarzschild–de Sitter black holes from Rényi statistics

It has been known that the Schwarzschild-de Sitter (Sch-dS) black hole may not be in thermal equilibrium and also be found to be thermodynamically unstable in the standard black hole thermodynamics. In the present work, we investigate the possibility to realize the thermodynamical stability of the Sch-dS black hole as an effective system by using the R\'{e}nyi statistics, which includes the non-extensive nature of black holes. Our results indicate that the non-extensivity allows the black hole to be thermodynamically stable which gives rise to the lower bound on the non-extensive parameter. By comparing the results to ones in the separated system approach, we find that the effective temperature is always smaller than the black hole horizon temperature and the thermodynamically stable black hole in effective approach is always larger than one in separated approach at a certain temperature. There exists only the zeroth-order phase transition from the the hot gas phase to the black hole phase for the effective system while it is possible to have the transition of both the zeroth order and the first order for the separated system.

Zeroth-order phase transition in the Blume-Emery-Griffiths model without bilinear exchange coupling.

We study the simplified Blume-Emery-Griffiths model without bilinear exchange coupling both in the microcanonical ensemble and in the canonical ensemble. This model can exhibit a zeroth-order phase transition in the microcanonical ensemble accompanied by a finite entropy jump. However, this singularity in entropy cannot be observed in the canonical ensemble, which illustrates the ensemble inequivalence. Moreover, the global phase diagram of this model is given in both ensembles.

Extended phase space thermodynamics for third-order Lovelock black holes with nonmaximally symmetric horizons

We study thermodynamics and critical behaviors of higher-dimensional Lovelock black holes with non-maximally symmetric horizons in the canonical ensemble of extended phase space. The effects from non-constancy of the horizon of the black hole via appearing two chargelike parameters in thermodynamic quantities of third-order Lovelock black holes are investigated. We find that Ricci flat black holes with nonconstant curvature horizon show critical behavior. This is an interesting feature that is not seen for any kind of black hole in Einstein or Lovelock gravity in the literature. We examine how various interesting thermodynamic phenomena such as standard first-order small-large black hole phase transition, a reentrant phase transition, or zeroth order phase transition happens for Ricci flat, spherical, or hyperbolic black holes with nonconstant curvature horizon depending on the values of Lovelock coefficient and chargelike parameters. While for a spherical black hole of third order Lovelock gravity with constant curvature horizon phase transition is observed only for $7\leq d \leq11$, for our solution criticality and phase transition exist in every dimension. With a proper choice of the free parameters, a large-small-large black hole phase transition occurs. This process is accompanied by a finite jump of the Gibbs free energy referred to as a zeroth-order phase transition. For the case $\kappa=-1$ a novel behavior is found for which three critical points could exist.

Static spherically symmetric black hole’s solution in Einstein–Maxwell–Yang–Mills-dilaton theory

In this work a static spherically symmetric black hole’s solution within the Einstein–Maxwell–Yang–Mills-dilaton theory is derived. The obtained solution is examined, in particular, we have calculated the Kretschmann scalar which allowed us to characterize singularity points. Using the obtained black hole’s solution we have studied its thermodynamics. Namely, the temperature was calculated, the first law was written, and the heat capacity was studied. The extended thermodynamics approach is utilized to obtain the equation of state. Within the extended thermodynamics the Gibbs free energy is derived and investigated. The analysis of the Gibbs free energy shows that below the critical temperature besides the first-order phase transition in addition the zeroth-order phase transition occurs, what is typical for other types of black holes with dilaton fields. Finally, we have shown that the critical exponents take the same values as for other types of the dilaton black holes.

Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions – a potential-theoretic characterization

We give a potential-theoretic characterization of measures μ0 which have the property that the Coulomb gas, defined with respect to the prior μ0, is “well-behaved” and similarly for more general Riesz gases. This means that the laws of the empirical measures of the corresponding random point process satisfy a Large Deviation Principle with a rate functional which depends continuously on the temperature, in the sense of Gamma-convergence. Equivalently, there is no zeroth-order phase transition at zero temperature, in the mean field regime. This is shown to be the case for the Hausdorff measure on a compact Lipschitz hypersurface, as well as Lesbesgue measure on a bounded Lipschitz domain. We also provide constructions of priors μ0, absolutely continuous with respect to Lebesgue measure on a smoothly bounded domain, such that the corresponding 2d Coulomb exhibits a zeroth-order phase transition. This is based on relations to Ullman’s criterion in the theory of orthogonal polynomials and Bernstein-Markov inequalities.

Static dilatonic black hole with nonlinear Maxwell and Yang–Mills fields of power-law type

Static spherically symmetric black hole solution is obtained in the framework of Einstein-dilaton theory with nonlinear Maxwell and Yang-Mills fields of power-law type. It is observed that black hole might have two horizons similarly as it takes place for linear gauge fields case. Thermodynamics of the black hole is studied, namely the behaviour of temperature is examined and the first law is written. The concept of extended phase space is also utilized, namely we have written and analyzed the equation of state for the black hole and examined the Gibbs free energy. The Gibbs free energy shows that there is the first order phase transition if the temperature or the pressure are below their critical values and coupling parameters are relatively small. Increasing of the coupling parameters might give rise to appearance of a domain with the zeroth order phase transition, the existence of the latter one is specific for other types of dilatonic black holes. Prigogine-Defay ratio has been calculated, it shows that at the critical point the phase transition is not exactly of the second order, it is closer to the glass-type phase transition since the Prigogine-Defay ratio is not equal to one.

Zeroth order phase transition induced by ergodicity breaking in a mean-field system

A spin chain model with mean-field interactions is studied within the microcanonical ensemble. Under local microcanonical dynamics, gaps in the space of extensive variables can be open up leading to the ergodicity breaking of this system. As a consequence, our mean-field system can exhibit the zero-order phase transition accompanied with an entropy jump at the transition point. Moreover, the global phase diagram of the system is constructed.

Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

We investigate a new class of [Formula: see text]-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher-dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth-order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.

Range of novel black hole phase transitions via massive gravity: Triple points and N -fold reentrant phase transitions

Massive gravities in anti-de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in $d$-dimensional spacetime reduces to a polynomial equation of degree $(d-4)$, which yields up to $n=(d-4)$ critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in $d \ge 7$), and a new phenomenon we call an $N$-fold reentrant phase transition, in which several ($N$) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zeroth-order phase transitions (in $d \ge 8$), as well as Van der Waals transitions (in $d \ge 5$) and reentrant (in $d \ge 6$) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.

Finely split phase transitions of rotating and accelerating black holes

We investigate the thermodynamic phase behaviour of rotating and slowly accelerating AdS black holes. While we find some similarities with the non-rotating charged counterparts, such as the peculiar phenomena of "snapping swallow tails" we also find subtle but significant distinctions that can be attributed to a qualitatively modified parameter space of the solution. Consequently the zeroth order phase transition now occurs over a range of pressures, mini-entropic black holes no longer exist in the regime of slow acceleration, and the "no black hole region" emerges continuously---from a zero temperature extremal black hole. The formerly equal transition pressure now experiences a fine splitting, as the emergence of a no black hole region and the zeroth-order phase transition appear at different pressures, different also from the termination pressure of the first order phase transition. This has the further effect of admitting reentrant phase transitions that can be achieved in two ways, either by varying the temperature at fixed pressure or varying the pressure at fixed temperature.

Snapping swallowtails in accelerating black hole thermodynamics

The thermodynamic behaviour of a charged and accelerating AdS black hole is studied in the context of extended phase space with variable cosmological constant. When compared to the charged AdS black hole without acceleration, a remarkable new feature of ‘snapping swallowtails’ appears. Namely, for any black hole with charge Q and any string tension causing the acceleration of the black hole, there exists a transition pressure at which the standard swallowtail ‘snaps’, causing the branch of low temperature black holes to completely disappear, leading to a pressure induced zeroth order phase transition between small and large black holes. For intermediate values of the string tension, we also observe a reentrant phase transition, as the small black hole changes to a large one and then back to small, as the pressure decreases, crossing the coexistence line of the two phases several times. We also find a new class of ‘mini-entropic’ black holes, whose isoperimetric ratio becomes unbounded in a certain region of parameter space.