Second-order Phase Transition Point Research Articles

Electrically charged black holes in gravity with a background Kalb–Ramond field

We derive the exact solutions for electrically charged black holes both in the absence and presence of a cosmological constant in the gravitational theory with Lorentz violation induced by a background Kalb–Ramond (KR) field. The corresponding thermodynamic properties are investigated. It is found that the standard first law of thermodynamics and the Smarr formula remain valid for the charged KR black holes. Nevertheless, the Lorentz-violating effect influences their ranges of local thermodynamic stability and the first- and second-order phase transition points. Furthermore, to examine the impact of Lorentz violation on the motion of test particles in the spacetime, we analyze the shadow and the innermost stable circular orbit (ISCO) of these black holes. Our results reveal that both the shadow and ISCO radii exhibit a high sensitivity to the Lorentz-violating parameter ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, with a decrease observed as ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document} increases.

Nonlinearly charged asymptotically massive Reissner-Nordström black holes in de Rham-Gabadadze-Tolley massive gravity theory

Two novel classes of nonlinearly charged black hole (BH) solutions are introduced in the context of massive gravity theory, which are coupled to the logarithmic and exponential theories of nonlinear electrodynamics. The solutions can produce one-horizon, two-horizon, extreme, and naked singularity BHs with the massive Reissner-Nordstr\"om BHs' asymptotic behavior. The BHs' conserved and thermodynamic quantities are calculated under the influence of both massive gravitons and nonlinear electrodynamics. Through a Smarr-type mass formula, it is shown that these quantities satisfy the standard form of the thermodynamical first law. Thermal stability of the massive BHs is investigated using the canonical ensemble and geometrical methods, separately. The first- and second-order phase transition points, and the size of those BHs which remain locally stable, are determined. Then, the results of these alternative approaches are compared. By calculating the Gibbs free energies, global stability or Hawking-Page phase transition of the BHs is studied. The points at which the phase transition takes place and the conditions under which the BHs are globally stable are characterized. The critical behavior of the BHs is studied in the extended phase space by considering the thermodynamic pressure proportional to the cosmological constant.

Group percolation in interdependent networks with reinforcement network layer.

In many real-world interdependent network systems, nodes often work together to form groups, which can enhance robustness to resist risks. However, previous group percolation models are always of a first-order phase transition, regardless of the group size distribution. This motivates us to investigate a generalized model for group percolation in interdependent networks with a reinforcement network layer to eliminate collapse. Some backup devices that are equipped for a density ρ of reinforced nodes constitute the reinforcement network layer. For each group, we assume that at least one node of the group can function in one network and a node in another network depends on the group to function. We find that increasing the density ρ of reinforcement nodes and the size S of the dependency group can significantly enhance the robustness of interdependent networks. Importantly, we find the existence of a hybrid phase transition behavior and propose a method for calculating the shift point of percolation types. The most interesting finding is the exact universal solution to the minimal density ρ of reinforced nodes (or the minimum group size S) to prevent abrupt collapse for Erdős-Rényi, scale-free, and regular random interdependent networks. Furthermore, we present the validity of the analytic solutions for a triple point ρ (or S ), the corresponding phase transition point p , and second-order phase transition points p in interdependent networks. These findings might yield a broad perspective for designing more resilient interdependent infrastructure networks.

Thermodynamic phase transition and global stability of the regular Hayward black hole surrounded by quintessence

In this work, we investigate the thermodynamic and the stability of the regular Hayward black hole surrounded by quintessence. Using the metric of the black hole surrounded by quintessence and the new approach of the holographic principle, we derive the expression of the Unruh–Verlinde temperature. Hawking temperature and specific heat are derived using the first law of black holes thermodynamics. Gibbs free energy is also evaluated. The behaviors of these quantities show that, the parameter of the regular Hayward black hole [Formula: see text] induces a decreasing of the Hawking temperature of the black hole, and that decrease is accentuated when increasing the magnitude of [Formula: see text] and the normalization factor related to the density of quintessence. For the lower entropies, the black hole passes from the unstable phase to the stable one by a first-order thermodynamics phase transition. When increasing the entropy, a second phase transition occurs. This new phase transition is a second-order thermodynamics phase transition and brings the black hole to unstable state. It results that, when increasing of magnitude of [Formula: see text], the phase transition points are shifted to the higher entropies. Moreover, the phenomena of phase transitions are preserved by adding the quintessence. Furthermore, when increasing the normalization factor of quintessence, the first-order transition point is shifted to higher entropies, while the second-order thermodynamics phase transition point is shifted to lower entropies.

Lattice fluid with attractive interaction between nearest neighbors and repulsive interaction between next-next-nearest neighbors on simple cubic lattice

The lattice system with competing interactions (attractive between nearest neighbors and repulsive between next-next-nearest neighbors) on a simple cubic lattice is studied. It is shown that the competing interactions lead to the order-disorder phase transitions. The geometric order parameter for localizing the second-order phase transition points is introduced. With its help the critical value of the interaction parameter was established, and the phase diagram of the system was constructed. An analytical quasi-chemical (QChA) approximation for evaluation of the equilibrium parameters of the system is proposed. The chemical potential, the thermodynamic factor, and the correlation functions are determined both within the framework of the developed approximate approach and as a result of the Monte Carlo simulation of the lattice system. The obtained dependence of the thermodynamic factor of the system on concentration indicates a strong suppression of fluctuations, characteristic for an ordered state. In turn, the complex nature of the concentration dependence of the correlation functions reflecting the structural features of the system demonstrates the important contribution of competing interactions. The proposed analytical approach allows one to correctly describe the qualitative features of the structural properties of systems with competing interactions and can be used to quantify the thermodynamic characteristics of these systems.

Phase diagrams and magnetic properties of a ferrimagnetic Ising bilayer superlattice: A Monte Carlo study

Monte Carlo simulation has been used to study the magnetic and thermodynamic properties of a ferrimagnetic mixed spin-1 and spin-3/2 Ising bilayer superlattice system on the honeycomb structure. The ground state phase diagrams of the system have been obtained for different single-ion anisotropies and exchange couplings. The system exhibits characteristic critical behaviors such as compensation points, the first- and second-order phase transition points as well as the tricritical points. The effects of the single-ion anisotropies and the exchange couplings on the magnetization, the susceptibility, the internal energy, the specific heat and the hysteresis loops are discussed in detail. Lots of interesting magnetic phenomena have been found, originating from the competitions among the anisotropies, the exchange couplings, the temperature and the external magnetic field. In particular, multiple cycle hysteresis loops behaviors such as the double and triple hysteresis loops have been discovered. Our results are in excellent agreement with previous theoretical studies.

Polaron in the dilute critical Bose condensate

The properties of an impurity immersed in a dilute D-dimensional Bose gas at temperatures close to its second-order phase transition point are considered. Particularly by means of the 1/N-expansion, we calculate the leading-order polaron energy and the damping rate in the limit of vanishing boson–boson interaction. It is shown that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit, signalling the non-analytic behavior of the impurity spectrum and pole-free structure of the polaron Green’s function in the infrared region, respectively.

Configurational entropy of charged AdS black holes

When we consider charged AdS black holes in higher dimensional spacetime and a molecule number density along coexistence curves is numerically extended to higher dimensional cases. It is found that a number density difference of a small and large black holes decrease as a total dimension grows up. In particular, we find that a configurational entropy is a concave function of a reduced temperature and reaches a maximum value at a critical (second-order phase transition) point. Furthermore, the bigger a total dimension becomes, the more concave function in a configurational entropy while the more convex function in a reduced pressure.

Social contagions on interdependent lattice networks

Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.

Holographic entanglement entropy in insulator/superconductor transitions with dark matter sector

We generalize the Stückelberg holographic superconductor model by including dark matter sector in the five-dimensional AdS soliton space–time beyond the probe limit. We study phase transitions with large charge of the scalar field through the condensation of the scalar operator and the holographic topological entanglement entropy of the system. We find that the entanglement entropy is a good probe of the order of phase transitions and second-order critical phase transition points. By investigating the behaviors of the entanglement entropy, we show that the larger coupling parameter [Formula: see text] makes the first-order phase transition more difficult to happen. In all, we conclude that the entanglement entropy can be used to study the effects of the dark matter sector in this general insulator/superconductor system.

Second-order phase transition in the Heisenberg model on a triangular lattice with competing interactions

We discover an example where the dissociation of the Z2 vortices occurs at the second-order phase transition point. We investigate the nature of phase transition in a classical Heisenberg model on a distorted triangular lattice with competing interactions. The order parameter space of the model is SO(3)xZ2. The dissociation of the Z2 vortices which comes from SO(3) and a second-order phase transition with Z2 symmetry breaking occur at the same temperature. We also find that the second-order phase transition belongs to the universality class of the two-dimensional Ising model.

Adaptation of the modified pulse method for determination of thermal diffusivity of solids in the vicinity of the second-order phase transition points

Abstract The paper presents the adaptation of the modified pulse method for investigating temperature characteristics of thermal diffusivity in the vicinity of the second-order phase transition points. The principle of the adaptation consists in the modified in relation to the original method, development of the characteristics of temperature changes between boundary surfaces of a flat-parallel specimen after the laser shot onto its front surface. The application of this adaptation was illustrated with investigation into thermal diffusivity of nickel (99.9% wt) in the temperature range of 20-380◦C. In all cases the measurement error was less than 3%, and the averaging interval for the measured values of thermal diffusivity was not greater than 1.2 K.

The Earth as a living planet: human-type diseases in the earthquake preparation process

Abstract. The new field of complex systems supports the view that a number of systems arising from disciplines as diverse as physics, biology, engineering, and economics may have certain quantitative features that are intriguingly similar. The Earth is a living planet where many complex systems run perfectly without stopping at all. The earthquake generation is a fundamental sign that the Earth is a living planet. Recently, analyses have shown that human-brain-type disease appears during the earthquake generation process. Herein, we show that human-heart-type disease appears during the earthquake preparation of the earthquake process. The investigation is mainly attempted by means of critical phenomena, which have been proposed as the likely paradigm to explain the origins of both heart electric fluctuations and fracture-induced electromagnetic fluctuations. We show that a time window of the damage evolution within the heterogeneous Earth's crust and the healthy heart's electrical action present the characteristic features of the critical point of a thermal second-order phase transition. A dramatic breakdown of critical characteristics appears in the tail of the fracture process of heterogeneous system and the injured heart's electrical action. Analyses by means of Hurst exponent and wavelet decomposition further support the hypothesis that a dynamical analogy exists between the geological and biological systems under study.

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice ‘thermodynamic’ structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with the arbitrary scalar curvature 2k in Hořava–Lifshitz gravity at the Lifshitz point z = 3. The analysis is done using the canonical ensemble framework, i.e. the charge is kept fixed. We find (a) for both k = 0 and k = 1, there is no phase transition, (b) while k = −1 case exhibits the second-order phase transition within the physical region of the black hole. The critical point of second-order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.

Holographic superconductor models in the non-minimal derivative coupling theory

We study a general class of holographic superconductor models via the Stückelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein's tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical exponents near the second-order phase transition point. Moreover, we compute the electrical conductivity using the probe approximation and check the ratios ωg/Tc for the different coupling parameters.

General holographic superconductor models with Born–Infeld electrodynamics

A general class of holographic superconductor models in Schwarzschild AdS black hole with the Born–Infeld electrodynamics is investigated. It is found that the Born–Infeld coupling parameter affects the critical temperature, the order of phase transitions, the conductivity and the critical exponents near the second-order phase transition point. It is also noted that both the position of the conductivity coherence peak and the ratio of the gap frequency in conductivity to the critical temperature depend on the model parameters and the Born–Infeld coupling parameter.

Temperature and thermodynamic geometry of the Kerr—Sen black hole

This paper studies the thermodynamic properties of the Kerr—Sen black hole from the viewpoint of geometry. It calculates the temperature and heat capacity of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the curvature scalar of Weinhold curvature implies no information about the phase transition while the Ruppeiner one does. But they both carry no information about the second-order phase transition point reproduced from the capacity. Besides, the Legendre invariant metric of the Kerr—Sen black hole has been discussed and its scalar curvature gives the information about the second-order phase transition point.

Effects of flavor-symmetry violation from staggered fermion lattice simulations of graphene

We analyze the effects of flavor splitting from staggered fermion lattice simulations of a low-energy effective theory for graphene. Both the unimproved action and the tadpole-improved action with a Naik term show significant flavor-symmetry breaking in the spectrum of the Dirac operator. Note that this is true even in the vicinity of the second-order phase transition point where it has been argued that the flavor-symmetry breaking should be small due to the continuum limit being approached. We show that at weaker couplings the flavor splitting is drastically reduced by stout link smearing, while this mechanism is ineffective at the stronger couplings relevant to suspended graphene. We also measure the average plaquette and describe how it calls for a reinterpretation of previous lattice Monte Carlo simulation results, due to tadpole improvement. After taking into account these effects, we conclude that previous lattice simulations are possibly indicative of an insulating phase, although the effective number of light flavors could be effectively less than two due to the flavor-splitting effects. If that is true, then simulations with truly chiral fermions (such as overlap fermions) are needed in order to settle the question.

Simulating Lattice Spin Models on Graphics Processing Units.

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often the large computational effort needed when approaching critical points. In this work, it is shown how such simulations can be accelerated with the use of NVIDIA graphics processing units (GPUs) using the CUDA programming architecture. We have developed two different algorithms for lattice spin models, the first useful for equilibrium properties near a second-order phase transition point and the second for dynamical slowing down near a glass transition. The algorithms are based on parallel MC techniques, and speedups from 70- to 150-fold over conventional single-threaded computer codes are obtained using consumer-grade hardware.

Thermodynamic geometry of the Garfinkle–Horowitz–Strominger dilaton black hole

This paper studies the thermodynamic properties of the Garfinkle–Horowitz–Strominger dilaton black hole from the viewpoint of geometry. It calculates the heat capacity and the temperature of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the scalar curvature of the Weinhold geometry consists with the first-order transition point reproduced from the capacity, while the Ruppeiner one is both in accordance with the first-order and the second-order phase transition points reproduced from the capacity.