Critical Exponents Research Articles

Triple points and phase transitions of D-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein–Gauss–Bonnet gravity

By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic AdS black holes (BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet (EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals (vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions. Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic AdS BHs with quasitopological electromagnetism in Einstein–Born–Infeld (EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D 105 104048 (2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic AdS BHs with quasitopological electromagnetism in EGB gravity.

Critical behavior and Joule-Thomson expansion of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state* *Supported by the Doctoral Foundation of Zunyi Normal University of China (BS [2022]07, QJJ-[2022]-314), and the National Natural Science Foundation of China (12265007, 12264061). The research partially was supported by the Long-Term Conceptual Development of a University of Hradec Králové

By considering the concept of a unified single fluid model, referred to as modified Chaplygin gas (MCG), which amalgamates dark energy and dark matter, we explore the thermodynamic characteristics of charged anti-de Sitter (AdS) black holes existing in an unconventional fluid accompanied by MCG. To accomplish this objective, we derive the equations of state by regarding the charge as a thermodynamic variable. The effects of MCG parameters on the critical thermodynamic quantities ( , , ) are examined, followed by a detailed analysis of the diagram. To provide a clearer explanation of the phase transition, we present an analysis of the Gibbs free energy. It is important to note that if the Hawking temperature exceeds the critical temperature, a distinct pattern is observed known as swallowtail behavior. This indicates that the system undergoes a first-order phase transition from a smaller black hole to a larger one. The critical exponent of the system is found to be in complete agreement with that of the van der Waals fluid system. Furthermore, we investigate the impact of MCG parameters and black hole charge on Joule-Thomson (J-T) expansion in the extended phase space. The J-T coefficient is examined to pinpoint the exact region experiencing cooling or heating, and the observation reveals that the presence of negative heat capacity results in the occurrence of a cooling process. The impact of MCG on the inversion curve of charged black holes exhibits a striking resemblance to that observed in most multi-dimensional black hole systems. In addition, it is worth noting that certain parameters exert a significant influence on the ratio . For specific values of the MCG parameters, the ratio is consistent with the charged AdS black hole. The parameters γ and β have a non-negligible effect on the isenthalpic curve.

Hysteresis-free reversible magnetocaloric effect and critical behavior of Ni39.56Fe7.27Co2.97Mn40.65Sn9.55 full heusler alloy

Utilizing the magnetocaloric effect (MCE), magnetic refrigeration technology offers an advantage over traditional gas-based refrigerators, which produce harmful gases. Herein, we study the MCE and critical magnetic behavior of Fe and Co substituted Ni39.56Fe7.27Co2.97Mn40.65Sn9.55 Heusler alloy near the paramagnetic (PM) to ferromagnetic (FM) transition temperature. With Fm3̅m space group, the present sample crystallizes in cubic L21 structure. Arrott plots and hysteresis-free continuous phase transition confirm a second-order transition from FM to PM. Again, this second-order transition is verified by collapsing scaled entropy curves for various fields into a single universal curve. The critical exponent values obtained using several analytical techniques, like the Kouvel-Fisher method, modified Arrott plot, and critical isotherm, correspond to the mean-field theory universality class having long-range ordering. The above findings suggest our sample to be a suitable magnetic refrigerant by overcoming the difficulty of obtaining a reversible and high value of magnetic entropy change along with substantial relative cooling power across the second-order phase transition.

Normalized solutions to the Kirchhoff Equation with triple critical exponents in [formula omitted

In this paper, we investigate the normalized solutions for the nonlinear critical Kirchhoff equations with combined nonlinearities: −a+b∫RN|∇u|2dxΔu=λu+μ|u|u+|u|2u,∫RNu2dx=c2,x∈RN,where N=4, λ, μ∈R and a, b, c>0 are constants. In R4, some interesting phenomena occur, which are, the L2-critical exponent for Δu is 2+4N=3, while the L2-critical exponent for (∫R4|∇u|2dx)Δu is equal to the Sobolev critical exponent, i.e., 2+8N=2NN−2=4. This paper investigates the case that the nonlinearity with triple critical term and proves the existence of a positive mountain-pass type normalized solution through variational methods and energy estimations.

Quantum criticality in chains of planar rotors with dipolar interactions.

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

The spin-5/2 Blume–Capel model by mean-field approach and renormalization group theory

The spin-5/2 Blume–Capel model was studied using the mean-field approximation and the Migdal–Kadanoff renormalization group method for two- and three-dimensional systems. We determined the phase diagrams in the (crystal field, temperature) plane where the system exhibited first- and second-order phase transitions as well as isolated critical, bicritical and triple points. In order to show first-order transitions at low temperature, we presented the total magnetization per site and the derivative of the free energy as a function of the crystal field. Moreover, the critical exponents of the system were calculated by linearizing the renormalization transformation at the vicinity of the second-order fixed points.

Coexisting magnetic interaction, critical behavior and magnetocaloric effect at high temperature in Fe50Ni50 soft ferromagnetic alloy

Herein, we report the structural, magnetic and magnetocaloric properties of Fe50Ni50 alloy prepared through the planetary ball-mill. Rietveld analysis of the X-ray profiles confirmed the cubic crystallographic phase with the Fm-3 m space group. The magnetic characterization demonstrates that Fe50Ni50 alloy exhibits the coexistence of magnetic interaction within the ferromagnetic phase with Curie temperature 762 K. The Arrott plot results confirmed the second-order nature of the alloy. Critical exponents were also determined using the modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis. Obtained results indicated coexisting magnetic behavior, i.e., long-range ferromagnetism and inhomogeneous magnetic state. This alloy also noted a significant magnetocaloric parameters, i.e., magnetic entropy change (−ΔSM ∼ 2.3 J/kg-K) and relative cooling power (RCP ∼ 230 J/kg) at 30 kOe applied field. Both parameters followed power law dependence of magnetic field, and the exponent value supports the ferromagnetic nature along with the coexisting magnetic state. By normalizing the ΔSM curve with rescaled temperature, a universal master curve is also constructed for this alloy, reiterating the second-order nature of the magnetic transition.

Criticality in the fracture of silica glass: Insights from molecular mechanics.

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

Enhancing Critical Digital Literacy of Preservice Preschool Teachers through Service Learning: The Moderator of Online Social Capital

This research delves into the examination of the correlation between service learning and critical digital literacy among preservice preschool teachers in Taiwan, with a particular emphasis on the role of online social capital. The survey took place in Taiwan with preservice preschool teachers who willingly completed a questionnaire. Initially, there were 416 data samples for further statistical analysis. This study utilizes literature reviews and theoretical reflections to examine the observed variables and factors in the “Service Learning and Critical Digital Literacy Scales” (SLCDL) questionnaire. To assess these aspects, a Chinese questionnaire is used, covering “service learning”, “critical digital literacy”, and “online social capital”. Using partial least squares analysis, researchers investigate the intricate interplay of online social capital in shaping the nexus between service learning experiences and the advance of critical digital literacy competencies. These results showed that service learning increased critical digital literacy among preservice preschool teachers, and online social capital played a mediating role in this relationship between service learning and critical digital literacy. We should actively encourage preservice preschool teachers to increase their critical awareness by understanding vulnerability and experiencing reality from the perspective of community partners. In addition, we need to provide more service learning opportunities that incorporate online social capital to enhance their critical digital literacy.

Critical behavior of cascading failures in overloaded networks.

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length ζ. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., ζ of the order of the system size L) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., ζ≪L) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.

Standard and inverse site percolation of triangular tiles on triangular lattices: Isotropic and perfectly oriented deposition and removal.

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of triangular tiles of side k (k-tiles) on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, k-tiles are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing k-tiles [composed by k(k+1)/2 monomers] from the lattice. Two schemes are used for the depositing and removing process: the isotropic scheme, where the deposition (removal) of the objects occurs with the same probability in any lattice direction; and the anisotropic (perfectly oriented or nematic) scheme, where one lattice direction is privileged for depositing (removing) the tiles. The study is conducted by following the behavior of four critical concentrations with the size k: (i)[(ii)] standard isotropic (oriented) percolation threshold θ_{c,k} (ϑ_{c,k}), which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θ_{c,k} (ϑ_{c,k}) is reached by isotropic (oriented) deposition of k-tiles on an initially empty lattice; and (iii)[(iv)] inverse isotropic (oriented) percolation threshold θ_{c,k}^{i} (ϑ_{c,k}^{i}), which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θ_{c,k}^{i} (ϑ_{c,k}^{i}) is reached after removing isotropic (completely aligned) k-tiles from an initially fully occupied lattice. The obtained results indicate that (1)θ_{c,k} (θ_{c,k}^{i}) is an increasing (decreasing) function of k in the range 1≤k≤6. For k≥7, all jammed configurations are nonpercolating (percolating) states and, consequently, the percolation phase transition disappears. (2)ϑ_{c,k} (ϑ_{c,k}^{i}) show a behavior qualitatively similar to that observed for isotropic deposition. In this case, the minimum value of k at which the phase transition disappears is k=5. (3) For both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus, a complementary property is found θ_{c,k}+θ_{c,k}^{i}=1 (and ϑ_{c,k}+ϑ_{c,k}^{i}=1), which has not been observed in other regular lattices. (4) Finally, in all cases, the jamming exponent ν_{j} was measured, being ν_{j}=1 regardless of the orientation (isotropic or nematic) or the size k considered. In addition, the accurate determination of the critical exponents ν,β, and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between one and five (three) for isotropic (nematic) deposition scheme, has the same universality class as the standard percolation problem.

Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

By considering the concept of the modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and dark matter, we construct a static, spherically charged black hole (BH) solution in the framework of General Relativity. The P–V criticality of the charged anti-de Sitter (AdS) BH with a surrounding MCG is explored in the context of the extended phase space, where the negative cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH phase transition is analogous to the van der Waals liquid/gas phase transition. Accordingly, along the P–V phase spaces, we derive the BH equations of state and then numerically evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities near criticality to a universal class. The use of geometrothermodynamic (GT) tools finally offers a new perspective on the discovery of the critical phase transition point. At this stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings are therefore non-trivial, as each GT class metric captures at least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with surrounding MCG.

On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity

We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: − Δ u = λ u p − u q in R N + 1 , where 0 < q < p < 1 and λ ∈ R. The approach is based on the Nehari manifold method supplemented by a one-sided constraint given through the functional of the suitable Pohozaev identity. The limit value of the parameter λ, where the approach is applicable, corresponds to the existence of periodic in one variable and compactly supported in the other variables least energy solutions. This value is found through the extrem values of nonlinear generalized Rayleigh quotients and the so-called curve of the critical exponents of p, q. Important properties of the solutions are derived for suitable ranges of the parameters, such as that they are not trivial with respect to the periodic variable and do not coincide with compactly supported solutions on the entire space R N + 1 .

Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems

We prove new optimal C1,α regularity results for obstacle problems involving evolutionary p-Laplace type operators in the degenerate regime p>2. Our main results include the optimal regularity improvement at free boundary points in intrinsic backward p-paraboloids, up to the critical exponent, α≤2/(p−2), and the optimal regularity across the free boundaries in the full cylinders up to a universal threshold. Moreover, we provide an intrinsic criterion by which the optimal regularity improvement at free boundaries can be extended to the entire cylinders. An important feature of our analysis is that we do not impose any assumption on the time derivative of the obstacle. Our results are formulated in function spaces associated to what we refer to as higher order or C1,α intrinsic interpolative geometries.

Object Detection in Remote Sensing Images Based on Adaptive Multi-Scale Feature Fusion Method

Multi-scale object detection is critical for analyzing remote sensing images. Traditional feature pyramid networks, which are aimed at accommodating objects of varying sizes through multi-level feature extraction, face significant challenges due to the diverse scale variations present in remote sensing images. This situation often forces single-level features to span a broad spectrum of object sizes, complicating accurate localization and classification. To tackle these challenges, this paper proposes an innovative algorithm that incorporates an adaptive multi-scale feature enhancement and fusion module (ASEM), which enhances remote sensing image object detection through sophisticated multi-scale feature fusion. Our method begins by employing a feature pyramid to gather coarse multi-scale features. Subsequently, it integrates a fine-grained feature extraction module at each level, utilizing atrous convolutions with varied dilation rates to refine multi-scale features, which markedly improves the information capture from widely varied object scales. Furthermore, an adaptive enhancement module is applied to the features of each level by employing an attention mechanism for feature fusion. This strategy concentrates on the features of critical scale, which significantly enhance the effectiveness of capturing essential feature information. Compared with the baseline method, namely, Rotated FasterRCNN, our method achieved an mAP of 74.21% ( 0.81%) on the DOTA-v1.0 dataset and an mAP of 84.90% (+9.2%) on the HRSC2016 dataset. These results validated the effectiveness and practicality of our method and demonstrated its significant application value in multi-scale remote sensing object detection tasks.

Sign‐changing solutions of fractional Laplacian system with critical exponent

This paper deals with the following fractional Laplacian system with critical exponent: where is a bounded smooth open connected set in is the fractional critical Sobolev exponent, and is the first eigenvalue of fractional Laplacian under the condition in . We prove that, for each fixed and slightly smaller than , the above system with admits a sign‐changing solution in the following sense: one component changes sign, while the other one is positive. Our result includes the lower dimensional case . Compared with the classical Laplacian case, our problem is nonlocal and the first component of the solution is sign‐changing, some new difficulties arise and new arguments and estimates should be introduced.

On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain

In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of the Caputo type. Moreover, we also give a result for nonexistence of global solutions to a wave equation with a nonlinear memory term in a bounded domain. The proof of blow-up results is based on the eigenfunction method and the asymptotic properties of solutions for an ordinary fractional differential inequality.

Multiple Solutions of a Nonlocal Problem with Nonlinear Boundary Conditions

In this article, we consider a class of nonlocal p(x)-Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem, we can prove the existence and multiplicity of solutions.

Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Abstract In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type − Δ u + u 2 ∗ 1 ∣ 4 π x ∣ u = μ f ( x ) ∣ u ∣ p − 2 u + g ( x ) ∣ u ∣ 4 u in R 3 , -\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2}u+g\left(x){| u| }^{4}u\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{3}, where μ > 0 \mu \gt 0 , 1 < p < 2 1\lt p\lt 2 , f ∈ L 6 6 − p ( R 3 ) f\in {L}^{\tfrac{6}{6-p}}\left({{\mathbb{R}}}^{3}) , and f , g ∈ C ( R 3 , R + ) f,g\in C\left({{\mathbb{R}}}^{3},{{\mathbb{R}}}^{+}) . Using Ekeland’s variational principle and a measure representation concentration-compactness of Lions, when g g has one local maximum point, we obtain two positive solutions for μ > 0 \mu \gt 0 small; while g g has k k strict local maximum points, we prove that the equation has at least k + 1 k+1 distinct positive solutions for μ > 0 \mu \gt 0 small by the Nehari manifold. Moreover, we show that one of the solutions is a ground state solution.

On a class of Kirchhoff type logarithmic Schrödinger equations involving the critical or supercritical Sobolev exponent

In this paper, we study a class of Kirchhoff type logarithmic Schrödinger equations involving the critical or supercritical Sobolev exponent. Such problems cannot be studied by applying variational methods in a standard way, because the nonlinearities do not satisfy the Ambrosetti-Rabinowitz condition and change sign. Moreover, the appearance of the logarithmic term makes the associated energy functional lose differentiable in the sense of Gateaux. By analyzing the structure of the Nehari manifold and developing some analysis techniques, the above obstacles are overcome in subtle ways and several existence result are obtained. Furthermore, we investigate the regularity, the monotonicity, and the symmetric properties of the solutions via the iterative technique and the moving plane method.