Joule–Thomson expansion of RN-AdS black hole immersed in perfect fluid dark matter

In this paper, we study the Joule–Thomson expansion for RN-Ad S black holes immersed in perfect fluid dark matter. As perfect fluid dark matter is one of the dark matter candidates, we are interested in how it influences the thermodynamic properties of black holes. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity as the thermodynamic volume, which give us more physical insights into the black hole. Moreover, we derive the thermodynamic definitions and study the critical behaviour of the black hole. Secondly,the explicit expression of Joule–Thomson coefficient is obtained from the basic formulas of the pressure, the volume, the entropy and the temperature. Then, we obtain the inversion curves in terms of charge Q and parameter λ. Furthermore, we analyse the isenthalpic curve in T–P graph with the cooling–heating region determined by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and compare the result with that in the RN-Ad S case.     

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in d S spacetime. Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system, we derive effective thermodynamic quantities of the system according to the first law of thermodynamics, and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α. It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system, and along with electric charge has an effect on the phase structure of the system,which is obvious, especially as the effective temperature is below the critical temperature. The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.     

Holographic superconductor in the analytic hairy black hole

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordström-AdS (HRNAdS) black holes. However, this transition unlikely occurs. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.     

Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space

In the extended phase space, we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of the Schwarzschild black hole surrounded by a spherical cavity. The results show that rainbow gravity has a very significant effect on the thermodynamic phenomena and phase structure of the black hole. It prevents the black hole from total evaporation and leads to a remnant with a limited temperature but no mass. Additionally, we restore the P − V criticality and obtain the critical quantities of the canonical ensemble. When the temperature or pressure is smaller than the critical quantities, the system undergoes two Hawking-Page-like phase transitions and one first-order phase transition, which never occurs in the original case. Remarkably, our findings demonstrate that the thermodynamic behavior and phase transition of the rainbow SC black hole surrounded by a cavity in the extended phase space are analogous to those of the Reissner–Nordström anti-de Sitter black hole. Therefore, rainbow gravity activates the effect of electric charge and cutoff factor in the evolution of the black hole.     

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain a universal exponent at the critical point of phase transition.     

Phase transition of charged black holes in massive gravity through new methods

Motivated by providing preliminary steps to understand the conception of quantum gravity, in this paper, we study the phase structure of a semiclassical gravitational system. We investigate the stability conditions and phase transition of charged black holes in massive gravity via canonical ensemble and geometrical thermodynamic approaches. We point out the effects of massive parameter on stability conditions of these black holes and show how massive coefficients affect the phase transition points of these black holes. We also study the effects of boundary topology on thermodynamical behavior of the system. In addition, we give some arguments regarding the role of higher dimensions and highlight the effect of the electric charge in thermodynamical behavior. Then, we extend our study to geometrical thermodynamic approach and show that it can be a successful method for studying the black hole phase transition. At last, by employing the relation between thermodynamical pressure and cosmological constant, critical behavior of the system and the effects of different parameters on critical values are investigated.     

Entropy of Higher-Dimensional Charged de Sitter Black Holes and Phase Transition

From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordströmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.     

P-V Criticality of Born-Infeld AdS Black Holes Surrounded by Quintessence

We discuss the P-V criticality and phase transition in the extended phase space of Born-Infeld AdS (BIAdS) black hole surrounded by quintessence dark energy, where the cosmological constant ∧ is identified with the thermodynamical pressure P. Comparing with Van der Waals(VdW)-like SBH/LBH phase transition of Born-Infeld AdS (BI-AdS) black hole, we find that the BI-AdS black hole surrounded by quintessence dark energy possesses lower critical temperature because of parameter a > 0, even disappears since the parameter a taking enough large values leads to T_c ≤ 0. Moreover, the interesting thermodynamic phenomenon of reentrant phase transition (RPT) are also observed, and the quintessence dark energy plays a similar role in this RPT.     

Correlated stability conjecture revisited

Correlated stability conjecture (CSC) proposed by Gubser and Mitra (2000, 2001)  and  linked the thermodynamic and classical (in)stabilities of black branes. The classical instabilities, whenever occurring, were conjectured to arise as Gregory–Laflamme (GL) instabilities of translationally invariant horizons. In Buchel (2005) [3] it was shown that the thermodynamic instabilities, specifically the negative specific heat, indeed result in the instabilities in the hydrodynamic spectrum of holographically dual plasma excitations. A counter-example of CSC was presented in the context of black branes with scalar hair undergoing a second-order phase transition (Friess et al., 2005 [4]). In this Letter we discuss a related counter-example of CSC conjecture, where a thermodynamically stable translationally invariant horizon has a genuine tachyonic instability. We study the spectrum of quasinormal excitations of a black brane undergoing a continuous phase transition, and explicitly identify the instability. We compute the critical exponents of the critical momenta and the frequency of the unstable fluctuations and identify the dynamical critical exponent of the model.     

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid–gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of \(T>T_c\), we have no phase transition. When \(T=T_c\), the system admits a second-order phase transition, while for \(T=T_\mathrm{f}<T_c\) the system experiences a first-order transition. Interestingly, for \(T_\mathrm{f}<T<T_c\) we observe a zeroth-order phase transition in the presence of a dilaton field. This novel zeroth-order phase transition occurs due to a finite jump in the Gibbs free energy which is generated by the dilaton–electromagnetic coupling constant, \(\alpha \), for a certain range of pressure.     

A Multi-parameter Model for Radio Dichotomy of Active Galactic Nuclei and Jets

Based on the coexistence of the Blandford-Znajek and magnetic coupling processes in black hole (BH) accretion disc, a multi-parameter model for jet powers and radio loudness of active galactic nuclei (AGNs) is studied. It turns out that radio-loudness of AGNs could be governed by five parameters: (i) the BH spin, (ii) a power-law index of the variation of the magnetic field on the disc; (iii) a parameter determining the position of the inner edge of the disc, (iv) the ratio of the pressure of the magnetic field on the horizon to the ram pressure of the innermost parts of an accretion flow, and (v) the ratio of the angular velocity of the open field lines to that of the horizon. The observed dichotomy between radio-loud and radio-quiet AGNs is well interpreted by the effects of the above parameters. Furthermore, we discuss the derivative of radio loudness of AGNs with respect to each parameter separately. In addition, the effect of the screw instability on radio loudness of AGNs is discussed.     

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

For charged black holes in Ho?ava–Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Ho?ava–Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Ho?ava–Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.     

<Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">v</Emphasis> criticality in the extended phase space of a noncommutative geometry inspired Reissner–Nordström black hole in AdS space-time

The P–v criticality and phase transition in the extended phase space of a noncommutative geometry inspired Reissner–Nordström (RN) black hole in Anti-de Sitter (AdS) space-time are studied, where the cosmological constant appears as a dynamical pressure and its conjugate quantity is thermodynamic volume of the black hole. It is found that the P–v criticality and the small black hole/large black hole phase transition appear for the noncommutative RN-AdS black hole. Numerical calculations indicate that the noncommutative parameter affects the phase transition as well as the critical temperature, horizon radius, pressure and ratio. The critical ratio is no longer universal, which is different from the result in the van de Waals liquid–gas system. The nature of phase transition at the critical point is also discussed. Especially, for the noncommutative geometry inspired RN-AdS black hole, a new thermodynamic quantity \(\varPsi \) conjugate to the noncommutative parameter \(\theta \) has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.     

Phase transitions in one-dimensional mechanical models of thermodynamics and the physics of the Hall bar system

We study one-dimensional mechanical systems by using a thermodynamic approach. In this framework we discuss the appearance of distinct thermodynamic phases corresponding to different types of trajectories for a charge carrier moving in a Hall bar, i.e. a channel patterned in a two-dimensional electron gas subject to a transverse magnetic field. In this device different kinds of orbits are allowed, cyclotron orbits, skipping orbits (when the particle collides with one channel wall), and traversing trajectories (when the particle collides with both channel walls). The passage from one type of orbits to the other can be characterized as a phase transition; so, in this system two different phase transitions can be identified.     

Thermodynamics of black holes in the quintessential phase space

Considering that the negative pressure of the accelerated expansion of the universe results from the cosmological constant or the dark energy quintessence, we use the dark energy quintessence to construct the "quintessential" phase space. In contrast to the previous discussion in which the cosmological constant is considered as the black hole (BH) phase transition pressure, in this analysis, we believe that the pressure results from quintessence. The characteristics of critical behavior, Gibbs free energy, and temperature behavior in quintessential phase space are investigated. We observe that the phase transition belongs to van der Waals phase transition within\begin{document}$ -1 <\omega_{\rm q}<-2/3 $\end{document}. If \begin{document}$ \omega_{\rm q} $\end{document}is within (–2/3, –1/3), the phase transition loses the large BH phase transition characteristics, which is caused by the later stage of the phase transition being completely dominated by quintessence dark energy with negative pressure. These results suggest that the quintessential phase space can be constructed with the pressure from the thermal quintessence, and it can be used as a new probe to explore the thermodynamics of BHs.     

Magnetic Phase Transitions in Nanoclusters and Nanostructures

New phenomena – the first order magnetic phase transitions were observed in nanoclusters and nanostructures. For isolated ferrihydrite nanoclusters (d ～ 1–2 nm) in porous materials, for α-,γ-Fe₂O₃ nanoclusters (d ～ 20–50 nm) and for composites of nanostructured metallic Eu with additives of α-, γ-Fe₂O₃ nanoclusters and adamantane the critical temperatures (T _C, T _N) and magnetic cluster critical sizes (R _cr) were determined by means of thermodynamic models and Mössbauer spectroscopy. The first order magnetic phase transitions (jump-like) proceed by such a way when magnetization and magnetic order disappear by jump without superparamagnetic relaxation. According to thermodynamic model predictions the cluster and interface defects were suggested to play the main role in magnetic behavior. Thus, for the defective α-, γ-Fe₂O₃ nanoclusters, at R ≤ R _cr, the presence of the first order (jump-like) magnetic phase transition was described in terms of magnetic critical size of cluster. The action of high pressure (up to 2 GPa) with shear (120–240°) was effective for defect generation and nanostructure formation. For nanosystems including iron oxide nanoclusters, adamantane and metallic europium and subjected to shear stress under high pressure loading the critical value of defect density was estimated by the study of the character of magnetic phase transition. First-to-second-order (nanostructured metallic Eu) and second-to-first-order (α-, γ-ferric oxide nanoclusters) changes of the character of magnetic phase transition were shown to accompany by the variation of critical temperatures compared to the corresponding bulk values.     

Quasi-one-dimensional quantum spin liquid in the Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.     

Magnetic ordering and phase transitions in planar antiferromagnetic systems with a Kagomé lattice

We study the process of magnetic ordering in planar antiferromagnetic systems with a Kagomé lattice. It is found that if the interaction between next-nearest-neighbor spins is taken into account, the heat capacity of such systems has a singularity at a finite temperature T. On the basis of a scaling analysis of finite-size systems we study the behavior of thermodynamic quantities in the neighborhood of a phase transition. We find that the phase transition at the critical point is due to discrete-and continuous-symmetry breaking, in which the long-range chiral order and the power-law translational spin order emerge simultaneously. Finally, we calculate the temperatures of the transition to different (with three and nine spins per unit cell) ordered states. Zh. éksp. Teor. Fiz. 113, 2209–2220 (June 1998)     

Metamagnetic phase transitions induced by static and pulsed fields in (Sm0.5Gd0.5)0.55Sr0.45MnO3 ceramics

It has been found that the magnetic susceptibility of (Sm_0.5Gd_0.5)_0.55Sr_0.45MnO₃ ceramic samples in zero external magnetic field exhibits a sharp peak near the temperature of 48.5 K with a small temperature hysteresis that does not depend on the frequency of measurements and is characteristic of the phase transition to an antiferromagnetic state with a long-range charge orbital ordering, which is accompanied by an increase in the magnetic susceptibility with a decrease in the temperature. The magnetization isotherms in static and pulsed magnetic fields at temperatures below 60 K demonstrate the occurrence of an irreversible metamagnetic transition to a homogeneous ferromagnetic state with a critical transition field independent of the measurement temperature, which, apparently, is associated with the destruction of the insulating state with a long-range charge ordering. In the temperature range 60 K ?? T ?? 150 K, the ceramic samples undergo a magnetic-field-induced reversible phase transition to the ferromagnetic state, which is similar to the metamagnetic transition in the low-temperature phase and is caused by the destruction of local charge/orbital correlations. With an increase in the temperature, the critical transition fields increase almost linearly and the field hysteresis disappears. Near the critical fields of magnetic phase transitions, small ultra-narrow magnetization steps have been revealed in pulsed fields with a high rate of change in the magnetic field of ??400 kOe/??s.     

Slow relaxation and avalanches in the spin-paramagnetic transition of a thin film granular superconductor

We report measurements of the superconducting to normal transition of ultra-thin granular Al films in parallel magnetic fields, H. The parallel critical field,H_c, in our samples is Pauli spin-paramagnetically limited. We find that the critical field transition goes from second-order to strongly first-order at a tricritical point, T_tr, near 250 mK. The first-order transition is characterized by a giant hysteresis in the critical field, ΔH_c 2.5 kG. In the hysteretic region we find that the films are far out of thermodynamic equilibrium and exhibit very slow, τ 10⁴s, glass-like, stretched-exponential relaxation. In addition, we observe significant avalanches. These observations are discussed in terms of a random array of Josephson junctions.