scholarly journals Phase Transitions, Geometrothermodynamics, and Critical Exponents of Black Holes with Conformal Anomaly

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jie-Xiong Mo ◽  
Wen-Biao Liu
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Phase Transitions ◽  
Scalar Curvature ◽  
Critical Exponents ◽  
Phase Structure ◽  
Scaling Laws ◽  
Canonical Ensemble ◽  
Conformal Anomaly ◽  
Transition Points

We investigate the phase transitions of black holes with conformal anomaly in canonical ensemble. Some interesting and novel phase transition phenomena have been discovered. It is shown that there are striking differences in both Hawking temperature and phase structure between black holes with conformal anomaly and those without it. Moreover, we probe in detail the dependence of phase transitions on the choice of parameters. The results show that black holes with conformal anomaly have much richer phase structure than those without it. There would be two, only one, or no phase transition points depending on the parameters. The corresponding parameter regions are derived both numerically and graphically. Geometrothermodynamics are built up to examine the phase structure we have discovered. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges. Furthermore, critical behaviors are investigated by calculating the relevant critical exponents. And we prove that these critical exponents satisfy the thermodynamic scaling laws.

Weinhold geometry and Ruppeiner geometry of black holes with conformal anomaly

2015 ◽  
Vol 30 (12) ◽  
pp. 1550061 ◽  
Author(s):  
Jie-Xiong Mo
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Specific Heat ◽  
Scalar Curvature ◽  
Phase Structure ◽  
Hawking Temperature ◽  
Conformal Anomaly ◽  
Transition Condition ◽  
Thermodynamic Geometry

The thermodynamic geometry of black holes with conformal anomaly has been investigated in this paper. We study two classical kinds of thermodynamic geometry. Namely, Weinhold geometry and Ruppeiner geometry. It is shown that the condition when Weinhold scalar curvature diverges is the same as the phase transition condition characterized by the divergence of specific heat. It is also shown that Ruppeiner scalar curvature not only reveals the phase structure but also contains the information of Hawking temperature. In a word, both Weinhold metric and Ruppeiner metric can correctly reproduce the phase structure of black holes even when conformal anomaly is taken into consideration.

Further investigation on phase transitions of Born–Infeld AdS black holes

2014 ◽  
Vol 29 (18) ◽  
pp. 1450087
Author(s):  
Jie-Xiong Mo ◽  
Gu-Qiang Li ◽  
Wen-Biao Liu
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Phase Structure ◽  
Canonical Ensemble ◽  
Standard Analysis ◽  
Ads Black Holes ◽  
The Impact ◽  
Constant Charge

In this paper, we further investigate the phase transitions of Born–Infeld AdS black holes in canonical ensemble. We take a different approach to investigate in detail the impact of the choice of parameters. Some interesting phase transition phenomena which has been ignored before are discovered. To examine the phase structure we find, we carry out the standard analysis of the behavior of free energy. We also apply the framework of geometrothermodynamics into Born–Infeld AdS black holes. It is shown that the Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat at constant charge diverges, which confirms the correctness of the phase structure we find. It is worth noting that although the phase structure shares similarity with RN-AdS black hole, it also has its unique characteristics due to influence of Born–Infeld electrodynamics.

scholarly journals Scalarized Einstein–Maxwell-scalar black holes in anti-de Sitter spacetime

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Guangzhou Guo ◽  
Peng Wang ◽  
Houwen Wu ◽  
Haitang Yang
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Phase Structure ◽  
Canonical Ensemble ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Maxwell Fields ◽  
Domain Of Existence ◽  
Black Hole Solutions

AbstractIn 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.

scholarly journals Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
S. H. Hendi ◽  
M. S. Talezadeh ◽  
Z. Armanfard
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Canonical Ensemble ◽  
Ricci Scalar ◽  
New Method ◽  
Thermodynamic Approach ◽  
Study Phase ◽  
Transition Points

Using the geometrical thermodynamic approach, we study phase transition of Brans–Dicke Born–Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies.

Extended phase space and thermodynamic geometry of topological Born–Infeld-dilaton black holes

2016 ◽  
Vol 25 (06) ◽  
pp. 1650062 ◽  
Author(s):  
A. Sheykhi ◽  
S. Hajkhalili
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Canonical Ensemble ◽  
Nonlinear Electrodynamics ◽  
Dilaton Field ◽  
Extended Phase ◽  
Thermodynamic Geometry ◽  
Transition Points ◽  
The Stability ◽  
Grand Canonical

We consider an [Formula: see text]-dimensional topological black holes of Einstein-dilaton gravity in the presence of Born–Infeld nonlinear electrodynamics. We investigate the thermal stability in the grand canonical ensemble and show that depending on the values of the parameters, these types of black holes can experience an instable phase and with changing of the metric parameters, the stability can be influenced. Also, we study the phase transition of these black holes via thermodynamic geometry approach and show that two types of phase transition can be occurred. Finally, we extend thermodynamical space by considering dilaton field as an extensive thermodynamic parameter and check the phase transition points.

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

scholarly journals CRITICAL BEHAVIOR IN THE ROTATING D-BRANES

1999 ◽  
Vol 14 (27) ◽  
pp. 1895-1907 ◽  
Author(s):  
RONG-GEN CAI ◽  
KWANG-SUP SOH
Keyword(s):  
Correlation Function ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Scaling Laws ◽  
Canonical Ensemble ◽  
Stable Boundary ◽  
Conformal Fields ◽  
Point Correlation ◽  
Point Correlation Function

We investigate the critical behavior near the thermodynamically stable boundary for the rotating D3-, M5- and M2-branes. The static scaling laws are found to hold. The critical exponents characterizing the scaling behaviors of susceptibilities are the same and all equal 1/2 in all cases. Using the scaling laws related to the correlation functions, we predict the critical exponents of the two-point correlation function of the corresponding conformal fields. We find that the stable boundary is shifted in the different ensembles and there does not exist the stable boundary in the canonical ensemble for the rotating M2-branes.

PHASE TRANSITION, GEOMETROTHERMODYNAMICS AND CRITICAL EXPONENTS OF BARDEEN BLACK HOLE

2014 ◽  
Vol 23 (04) ◽  
pp. 1450040
Author(s):  
JIE-XIONG MO
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Specific Heat ◽  
Critical Exponents ◽  
Transition Point ◽  
Scaling Laws ◽  
Phase Transition Point ◽  
Invariant Metrics ◽  
Thermodynamic Quantities ◽  
Transition Structure

In this paper, we investigate the phase transition of Bardeen black hole for the first time. First, we calculate thermodynamic quantities and correct the misuse of formula in former literature. Second, we investigate in detail the behavior of specific heat. We not only discuss the influence of parameter on phase transition, but also show the three-dimensional behavior of the specific heat. It is shown that phase transition takes place from a locally unstable large black hole to a locally stable small black hole. It is also shown that the location of phase transition point is proportional to the charge. Meanwhile, we study the behavior of the inverse of the isothermal compressibility and find that it diverges at the phase transition point. Thirdly, we build up geometrothermodynamics to examine the phase transition structure. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges, which leads to the conclusion that the Legendre invariant metrics can correctly produce the behavior of the phase transition structure. Furthermore, to gain a thorough understanding of critical behavior, we calculate the relevant critical exponents and examine the scaling laws. It is shown that they are in agreement with the scaling laws.

QUANTUM PHASE TRANSITIONS AND ENTANGLEMENT IN J1–J2 MODEL

2004 ◽  
Vol 15 (08) ◽  
pp. 1095-1103 ◽  
Author(s):  
RECEP ERYIĞIT ◽  
RESUL ERYIĞIT ◽  
YIĞIT GÜNDÜÇ
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Ground State ◽  
Abrupt Change ◽  
Quantum Phase Transitions ◽  
Nearest Neighbors ◽  
Competing Interactions ◽  
One Dimensional ◽  
Transition Points

We study ground state pairwise entanglement within one-dimensional spin-1/2 antiferromagnetic J1–J2 model with competing interactions. Contrary to some claims we found that frustration does not increase entanglement. Concurrence of nearest and next nearest neighbors are found to show abrupt change at phase transition points. We also show that the concurrence can be used to classify the phase diagram of the model in anisotropy–frustration plane.

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