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The state-of-the-art in the theory of self-organized criticality reveals that a certain inactivity precedes extreme events, which are located on the tail of the event probability distribution with respect to their sizes. The existence of the inactivity allows for the prediction of these events in advance. In this work, we explore the predictability of the Bak–Tang–Wiesenfeld (BTW) and Manna models on the square lattice as a function of the lattice length. For both models, we use an algorithm that forecasts the occurrence of large events after a fall in activity. The efficiency of the prediction can be universally described in terms of the event size divided by an appropriate power-law function of the lattice length. The power-law exponents are projected to be 2.75 and 3 for the Manna and BTW models respectively. The scaling with the exponent 2.75 is known for collapsing of the entire size-frequency relationship in the Manna model. However, the correspondence between events on different lattices in the BTW model requires a variety of exponents where 3 is the largest. This indicates that in thermodynamic limit, prediction does exist in the Manna but not in the BTW model, at least based on inactivity. The difference in the universality classes may underline the difference in the prediction. [ABSTRACT FROM AUTHOR]

The La0.9·0.1MnO2.9 compound were prepared by sol–gel method with the aim of obtaining a material with interesting magnetocaloric and thermoelectric properties. The prepared material crystallized in rhombohedric system with R-3c space group. In the magnetization vs. temperature graph, it is observed a paramagnetic (PM)-ferromagnetic (FM) transition with a Curie temperature TC of 209 K. From the fit of hysteresis cycle at 5 K, it is observed that the dominant contribution is ferromagnetic. A magnetic entropy change, calculated from the isothermal magnetization curves, was observed for the sample with a peak centered on TC. The total electronic density states (TDOS) show the coexistence of metallic behavior for spin-up states and semiconductor characteristic, with a Eg = 1.3 eV, for spin-down states. Thermoelectric properties analysis revealed promising behavior with ZT that assesses the efficacy of a compound in a thermoelectric field, reaching 1.1 at 420 K. [ABSTRACT FROM AUTHOR]

In this research work, samples of Pr0.8Sr0.2MnO3 were prepared using two methods: the conventional high-temperature ceramic method (sample R1) and the sol–gel method (sample R2) in order to form a composite. The Curie temperatures were found to be 161 K and 210 K for R1 and R2, respectively. We conducted a theoretical investigation of the magnetic and magnetocaloric (MC) properties of a composite constructed from R1 and R2 compounds to enhance the MC effect.The results suggest that our composite, with a Curie temperature evaluated at 190 K, could be a potential candidate for magnetic refrigeration. Refined values of the critical exponents β, γ, and δ, determined from the modified Arrott plots and the Kouvel–Fisher method, indicate that the behavior of the composite compound is consistent with the 3D Heisenberg model for T ≤ TC and with the mean-field model for T > TC. [ABSTRACT FROM AUTHOR]

This paper is concerned with the bifurcation properties of the standing wave solutions for the Schrödinger–Poisson system with doubly critical case The study of system (P ) is motivated by its important applications in many physical models, such as the quantum mechanical systems under external influences. Here, 3 ≤ N ≤ 6 , 0 < α < N , λ ∈ R , g is a nonnegative weight function, and 2 α ♯ and 2 α ∗ are the lower and upper Hardy–Littlewood–Sobolev critical exponents, respectively. Moreover, when N = 6 and 0 < α < 2 existence of the (weak) solutions of the system under consideration is also proved via the global bifurcation theorem due to Rabinowitz. [ABSTRACT FROM AUTHOR]

Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the integer quantum Hall (IQH) effects can be understood from the band topology of non-interacting electrons. We report a surprising super-universality of the critical behavior across all FQH and IQH transitions. Contrary to the anticipated state-dependent critical exponents, our findings reveal the same critical scaling exponent κ = 0.41 ± 0.02 and localization length exponent γ = 2.4 ± 0.2 for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent z ≈ 1. We have achieved this in ultra-high mobility trilayer graphene devices with a metallic screening layer close to the conduction channels. The observation of these global critical exponents across various quantum Hall phase transitions was masked in previous studies by significant sample-to-sample variation in the measured values of κ in conventional semiconductor heterostructures, where long-range correlated disorder dominates. We show that the robust scaling exponents are valid in the limit of short-range disorder correlations. The relationship between the integer and fractional quantum Hall states are of fundamental importance in condensed matter physics. Here, the authors report a universality of phase transitions in both regimes in ultraclean trilayer graphene samples. [ABSTRACT FROM AUTHOR]

We study the existence of solutions to the problem - Δ u + u p - M ∇ u q = 0 in Ω , (1) u = μ on ∂ Ω in a bounded domain Ω, where p > 1, 1 < q < 2, M > 0, μ is a nonnegative Radon measure in ∂Ω, and the associated problem with a boundary isolated singularity at a ∈ ∂Ω, - Δ u + u p - M ∇ u q = 0 in Ω , (2) u = 0 on ∂ Ω \ α. The difficulty lies in the opposition between the two nonlinear terms which are not on the same nature. Existence of solutions to (1) is obtained under a capacitary condition μ K ≤ c min cap 2 p , p ′ ∂ Ω , cap 2 - q q , q ′ ∂ Ω for\;all\;compacts\; K ⊂ ∂ Ω. Problem (2) depends on several critical exponents on p and q as well as the position of q with respect to 2 p p + 1 . [ABSTRACT FROM AUTHOR]

The investigation of site percolation on Sierpinski carpets is carried out through comprehensive numerical simulations. We utilize finite- size scaling theory, staying within the constraints of our computational resources, to determine critical exponents and percolation thresholds. Moreover, we employ an approach developed by Elliot et al. (Phys Rev C 6:3185, 1994; Phys Rev C 55:1319, 1997), which streamlines the process by eliminating the necessity of dealing with large lattices. This method facilitates the extraction of critical quantities that characterize the transition from a single generation within a given structure. By implementing this procedure, we enhance efficiency and accuracy in analyzing the percolation phenomenon on Sierpinski carpets. The obtained values of the percolation thresholds are plotted as a function of the fractal dimensions in order to determine the lower critical dimension of the site percolation problem which is calculated to be d c L = 1.52 . In addition, the behavior of the critical exponents as a function of the fractal dimension is also shown and discussed. [ABSTRACT FROM AUTHOR]

Mn5Ge3 compound is a well-established rare-earth-free magnetocaloric material with a near-room temperature magnetocaloric effect. Chemical modification could increase its relative cooling power and to achieve that we have substituted copper and synthesized Mn4.8Cu0.2Ge3 polycrystalline compound through arc-melting process. Mn4.8Cu0.2Ge3 is an itinerant ferromagnet with a second-order magnetic transition in the vicinity of room temperature. In comparison with the pure Mn5Ge3 compound, the temperature span of the magnetocaloric effect has widened, which is a favorable requirement in practical devices. The magnetization critical exponents were estimated through the modified Arrott plot and Kouvel-Fischer methods. An unconventional critical behavior was noticed in this compound, in which the critical exponents β and γ fall close to the standard 3D-XY and 3D-Ising models, respectively. On the other hand, the pure Mn5Ge3 single crystal shows 3D-Ising critical behavior, and the deviation from the standard universality class in Mn4.8Cu0.2Ge3 could be attributed to the modification in Mn–Mn distance induced by the copper. On analyzing the magnetic properties of Mn5-xCuxGe3 (x = 0.1, 0.2, and 0.3) series, we speculate that x = 0.2 compound breaks the series monotonicity due to the unique influence of Cu substitution on Mn–Mn interactions. [ABSTRACT FROM AUTHOR]

We investigate the multiplicity results of positive solutions for a Kirchhoff-type problems with supercritical and critical nonlinear terms in a ball. By employing the Nehari method and Lusternik–Schnirelmann category theory to an auxiliary problems, we note that there is a relationship between the number of maxima in the coefficient function of the critical term and the number of positive solutions for the problems. [ABSTRACT FROM AUTHOR]

Recent cellular-level volumetric brain reconstructions have revealed high levels of anatomic complexity. Determining which structural aspects of the brain to focus on, especially when comparing with computational models and other organisms, remains a major challenge. Here we quantify aspects of this complexity and show evidence that brain anatomy satisfies universal scaling laws, establishing the notion of structural criticality in the cellular structure of the brain. Our framework builds upon understanding of critical systems to provide clear guidance in selecting informative structural properties of cellular brain anatomy. As an illustration, we obtain estimates for critical exponents in the human, mouse and fruit fly brains and show that they are consistent between organisms, to the extent that data limitations allow. Such universal quantities are robust to many of the microscopic details of the cellular structures of individual brains, providing a key step towards generative computational models of the cellular structure of the brain, and also clarifying in which sense one animal may be a suitable anatomic model for another. Cellular-level partial brain reconstructions have revealed the anatomic complexity of the brains of multiple organisms. Here, the authors quantify aspects of this complexity, demonstrating that across organisms the cellular structure of the brain shows universal scaling properties associated with being in the vicinity of criticality. [ABSTRACT FROM AUTHOR]

In this paper, we prove the multiplicity and concentration behavior of complex-valued solutions for the following Kirchhoff–Schrödinger equation with magnetic field - (a ε 2 + b ε [ u ] A / ε 2) Δ A / ε u + V (x) u = f (| u | 2) u , x ∈ R 2 , where ε > 0 is a small parameter, the nonlinearity f is involved in critical exponential growth in the sense of Trudinger–Moser inequality and both V : R 2 → R and A : R 2 → R 2 are continuous potential and magnetic potential, respectively. Imposing a local constraint of potential V(x) first introduced from del Pino and Felmer, we get the multiplicity of solutions by way of the relationship between the number of the solutions and the topology of the set with V attaining the minimum. Our strategy of main proof is based on the variational methods combined with the penalization technique, the Trudinger–Moser inequality and Ljusternik–Schnirelmann theory, and our result is still new even without magnetic effect. [ABSTRACT FROM AUTHOR]

We have systematically investigated the critical behavior around paramagnetic-ferromagnetic (PM-FM) phase transition temperature, TC, and attempted to determine the Curie temperatures and critical exponents β, γ and δ of perovskite manganites La0.67Ba0.33–xSrxMnO3 (x = 0.1, 0.2 and 0.25).The TC determined from M(T) is observed to increase from 336.7 to 368.4 K, with Sr doping at Ba. The critical exponents β, γ and δ are determined from the magnetization, M(T,H), using Modified Arrott Plots for theoretically predicted models and critical M(H) isotherms at T = TC. From the critical exponents we have inferred that La0.67Ba0.33–xSrxMnO3 behave as a three-dimensional (3D) isotropic nearest heighbor Heisenberg ferromagnet in the critical region. We have further verified that the behavior of 3D isotropic nearest neighbor Heisenberg is in agreement with the values of exponent 'n' determined based on the relation between field dependent change in magnetic entropy at the Curie temperature, T = TC. Sr doping at Ba site in La0.67Ba0.33–xSrxMnO3 does not lead to any crossover in the type of magnetic interactions present in the materials, indicating a stable behavior of 3D isotropic nearest neighbor Heisenberg ferromagnet in the critical region. The differences in the values of parameters may be attributed to the complex nature of interactions present in these materials. [ABSTRACT FROM AUTHOR]

In this paper, the compensation characteristics and hysteresis loops of a ferrimagnetic mixed-spin diluted fullerene-like (XY)540 are studied based on Monte Carlo method. We show the ground-state phase diagrams in order to explore the stable configuration states. The temperature dependence of magnetization, magnetic susceptibility, internal energy, specific heat, and entropy are presented. The phase diagram including compensation temperature Tcomp and phase change temperature Tc is obtained. The multi-loop hysteresis phenomena under the influence of diverse physical parameters are observed. Finally, the critical exponents of the fullerene-like (XY)540 are obtained. [ABSTRACT FROM AUTHOR]

We consider the following singular quasilinear Schrödinger equations involving critical exponent - Δ u - α 2 Δ (| u | α ) | u | α - 2 u = θ | u | k - 2 u + | u | 2 ∗ - 2 u + λ f (u) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where 0 < α < 1 . By using the variational methods, we first prove that for small values of λ and θ , the above problem has infinitely many distinct solutions with negative energy. Besides, we point out that odd assumption on f is required; the problem has at least one nontrivial solution. Finally, a new modified technique is used to consider the existence of infinitely many solutions for far more general equations. [ABSTRACT FROM AUTHOR]

Many physical properties behave differently in disorder systems from the order one. The effects of atomic disorder on the magnetic properties have been explored on Co2TiSi and Co2TiAl full Heusler alloys. Co2TiSi crystallizes in an ordered L21 crystal symmetry, and Co2TiAl mainly possesses a B2 structure. The B2 disorder affects not only the magnetic ordering but also the saturation magnetization, causing the deviation from the Slater-Pauling prediction for Co2TiAl. The critical exponents of the magnetic phase transition have been analyzed by employing different techniques like, the Arrott plot, Kouvel–Fisher plot, critical isotherm analysis, scaling magnetic behavior, and magnetocaloric analysis as well. The calculated critical exponents are close to the mean field theory which implies long-range ferromagnetic ordering in Co2TiSi. However, the exchange interaction in Co2TiAl deviates from the long-range mean field theory. This may be due to the magnetic contribution of the B2-disordered phase. In addition to the magnetic ordering, the magnetocaloric analysis provides the applicability of Co2TiSi alloy as a low-cost, hysteresis-free magnetic refrigerant with a large working temperature near room temperature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups. [ABSTRACT FROM AUTHOR]

Near continuous phase transitions, universal power-law scaling, characterized by critical exponents, emerges. This behavior reflects the singular responses of physical systems to continuous control parameters like temperature or external fields. Universal scaling extends to non-equilibrium dynamics in isolated quantum systems after a quench, where time takes the role of the control parameter. Our research unveils critical scaling in time also during the relaxation dynamics of an open quantum system. Here we experimentally realize such a system by the spin of individual Cesium atoms dissipatively coupled through spin-exchange processes to a bath of ultracold Rubidium atoms. Through a finite-size scaling analysis of the entropy dynamics via numerical simulations, we identify a critical point in time in the thermodynamic limit. This critical point is accompanied by the divergence of a characteristic length, which is described by critical exponents that turn out to be unaffected by system specifics. The dynamics of a quantum system shows interesting features. Here the authors demonstrate critical scaling in the spin relaxation due to spin-exchange process in a system of impurity Cs atoms immersed in Rb atoms. [ABSTRACT FROM AUTHOR]

We investigate the critical behavior of Lifshitz black holes in Einstein-dilaton gravity in the context of spontaneous Lorentz symmetry breaking. Considering the effects of both the Bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new asymptotically Lifshitz charged solutions in (3 + 1) dimensions. We consider the longitudinal massive mode of Lorentz violation (LV) as thermodynamic pressure, leading us to establish an P - V extended phase space. Within this framework, we derive the equation of state P(T, V), and subsequently identify the critical points, which manifest as discontinuities in the specific heat at constant pressure. Following this, we compute the Gibbs free energy, revealing a first-order phase transition within the model. Finally, we determine the critical exponents, demonstrating their equivalence to those observed in the Van der Waals system. [ABSTRACT FROM AUTHOR]

The compensation behaviors and phase transitions of a new 3D fullerene-like polymer are explored by using Monte Carlo method. The ground-state phase diagrams and magnetization profiles are given, and the conditions for the occurrence of the compensation temperature Tcomp are obtained. As classified in Néel theory, N-type and P-type magnetization curves are found. To explore the changes in the transition temperature TC and the compensation temperature Tcomp induced by physical parameters, we also present the phase diagrams. Furthermore, the critical exponents of the system are calculated, and a good agreement can be achieved by comparing our results with others'. Finally, the triple hysteresis loops are discovered. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problems involving critical exponents and logarithmic nonlinearity. By using the constraint variational method, we show the existence of one least energy sign-changing solution. Moreover, we show that this energy is strictly larger than twice the ground energy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a gradient type term for the k-Hessian equation that extends for k > 1 the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan–Kramer change of variables. As applications, we ensure the existence of solutions for a new class of k-Hessian equation in the sublinear and superlinear cases for Sobolev type growth. The threshold for existence is obtained in some particular cases. In addition, for the Trudinger–Moser type growth regime, we also prove the existence of solutions under either subcritical or critical conditions. [ABSTRACT FROM AUTHOR]

In the present paper, we are concerned with the existence and multiplicity of normalized solutions of coupled Hartree–Fock system with upper critical exponent and lower power perturbation. This type system arises from the basic quantum chemistry model of small number of electrons interacting with static nuclei which can be approximated by Hartree or Hartree–Fock minimization problems. First, by constraint manifold methods and refined energy estimates, we prove the existence of ground and bound states normalized solutions for critical Hartree–Fock system. Then the precise asymptotic behaviors of two normalized solutions are also obtained. Finally, we discuss the orbital stability and finite time blow-up of the associated solitary wave solutions. [ABSTRACT FROM AUTHOR]

The phase diagram of a system with two order parameters, with n 1 and n 2 components, respectively, contains two phases, in which these order parameters are non-zero. Experimentally and numerically, these phases are often separated by a first-order "flop" line, which ends at a bicritical point. For n = n 1 + n 2 = 3 and d = 3 dimensions (relevant, e.g., to the uniaxial antiferromagnet in a uniform magnetic field), this bicritical point is found to exhibit a crossover from the isotropic n-component universal critical behavior to a fluctuation-driven first-order transition, asymptotically turning into a triple point. Using a novel expansion of the renormalization group recursion relations near the isotropic fixed point, combined with a resummation of the sixth-order diagrammatic expansions of the coefficients in this expansion, we show that the above crossover is slow, explaining the apparently observed second-order transition. However, the effective critical exponents near that transition, which are calculated here, vary strongly as the triple point is approached. [ABSTRACT FROM AUTHOR]

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material's critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit. Van der Waals antiferromagnets offer a unique platform for studying magnetism in reduced dimensions, however, the low dimensionality, combined with lack of net magnetization, renders investigation challenging with conventional experimental probes. Here, Houmes et al show how van der Waals antiferromagnets can be investigated via the resonances of a vibrating rectangular membranes of this material. [ABSTRACT FROM AUTHOR]

This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli et al. (Proc Am Math Soc 148:2579–2593, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we will fill the gap in the results of Jleli et al. (2020) for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define another critical exponent depending on the forcing term. [ABSTRACT FROM AUTHOR]

In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation where c > 0, 0 < μ < N, λ ∈ ℝ, A ∈ C1 (ℝN, ℝ). For p ∈ (2*,μ, p ¯ , we prove that the Choquard equation possesses normalized ground state solutions, and the set of ground states is orbitally stable. For p ∈ (p ¯ , 2 μ ∗) , we find a normalized solution, which is not a global minimizer. 2*μ and 2*,μ are the upper and lower critical exponents due to the Hardy–Littlewood–Sobolev inequality, respectively. p ¯ is the L2-critical exponent. Our results generalize and extend some related results. [ABSTRACT FROM AUTHOR]

As purchased, PVDF and MWCNT were used to synthesise PD by varying the volume fractions of MWCNT (fMWCNT) into the polymer matrix through the novel cold-pressing method. The structure, microstructure and the electrical properties of the samples were obtained through XRD, FESEM, and Impedance analyzer. The microstructures of the PD show the presence of two components, such as the spherulites of PVDF (retained due to the novel cold-pressing) and the distribution of MWCNT into the PVDF matrix. The extent of distribution of MWCNT in the PD increases and the clustering of MWCNT also increases with increase of fMWCNT. The PD undergo an insulator to metal transition (IMT), with a non-universal low percolation threshold (fc) value of fMWCNT = 0.006, attributed to the high aspect ratio of MWCNT and the adhesiveness/method of preparation of the PD. The scaling equations hold good in the critical region around IMT, and the non-universal critical exponents [s = 0.36 ± 0.03, s' = 1.26 ± 0.1] were obtained. Impedance, Nyquist and Modulus spectra for the PD have been implemented to understand the relaxation behaviour/microstructure of the samples. For fc, a broad relaxation, understood by a modified Kohlrausch, Williams and Watts (KWW) function, showing a non-Debye type relaxation associated with the universal stretched coefficient of β = 0.54 is obtained. The σeff with frequency obeys universal Jonscher's power law with exponent, k = 0.91 ± 0.01. [ABSTRACT FROM AUTHOR]

In this paper, we first construct one bubbling solution for a higher order prescribed curvature problem with periodic boundary condition in a strip. then, we prove the existence of periodic solution for the higher order prescribed curvature problem in R N , if the prescribed curvature function is periodic. The novelty of the paper is that we obtain the periodic solution directly without involving uniqueness and many complicated estimates. We believe our method will be helpful for other problems related to periodic solution and higher order equations. [ABSTRACT FROM AUTHOR]

A system of mutually consistent equations for ethane is developed that describes pressure , vapor density , liquid density , derivative , and heat of vaporization on the phase equilibrium line in the range of the triple point to the critical point. The system also includes apparent heat of vaporization , which is associated with heat of vaporization : . It is established on the basis of the thermodynamic analysis that (1) the condition of average diameter is fulfilled at each point of the saturation line except for the critical point, at which , and (2) the average diameter is reduced sharply in the interval of . The system of mutually consistent equations reproduces the phase equilibrium line of ethane within the experimental uncertainty data of Funke et al. (2002) in the range of the triple point ( , , ) to the critical point ( , , ). It also reproduces features of the critical point in accordance with the renormalization group (RG) theory developed by Zhou et al. (2022) for a system of asymmetric systems. Based on the Clausius–Clapeyron equation and renormalization group theory, an expression is obtained for the apparent heat of vaporization. Analysis of average diameter for two groups of complexes shows that (a) , , and , and (b) , , and , which correspond to values , , and obtained by Wang et al. (2013) in the RG theory and the modeling of experimental data for ethane on the saturation line. Based on the proposed system of mutually consistent equations, average diameter of ethane is found for complexes (a) and (b), and it is established that the average diameter determined on the basis of data by Funke et al. (2002) is given most accurately by the system of mutually consistent equations in the range of to with parameters , , and . [ABSTRACT FROM AUTHOR]

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension D ≤ 2. For long-range interactions with a power-law form (1/rα), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when α ≥ 2D. However, the situation for α ∈ (2, 4) at D = 2 is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of SU(2) symmetry in the ferromagnetic Heisenberg model with 1/rα-form long-range interactions at D = 2. We determine critical exponents through finite-size analysis for α < 3 (above the upper critical dimension with Gaussian fixed point) and 3 ≤ α < 4 (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope. [ABSTRACT FROM AUTHOR]

We present first calculations of critical spectral functions of the relaxational Models A, B, and C in the Halperin-Hohenberg classification using a real-time formulation of the functional renormalization group (FRG). We revisit the prediction by Son and Stephanov that the linear coupling of a conserved density to the non-conserved order parameter of Model A gives rise to critical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistent expansion schemes in the 1PI vertex functions as truncations of the effective average action suitable for real-time applications, and analyze in detail how the different critical dynamics are properly incorporated in the framework of the FRG on the closed-time path. We present results for the corresponding critical spectral functions, extract the dynamic critical exponents for Models A, B, and C, in two and three spatial dimensions, respectively, and compare the resulting values with recent results from the literature. [ABSTRACT FROM AUTHOR]

Abstract—This paper studies the development of approaches to expand the method for calculating the properties of liquid sodium in the region of overheating and at high temperatures. The expansion is carried out using the hypothesis of the linearity of isochores and interpolation of the properties of sodium on the saturation line using the theory of critical exponents. Using modified techniques, the position of the spinodal is calculated and an expression is given to estimate its position. A comparison is made with the available published data. Satisfactory agreement is obtained. [ABSTRACT FROM AUTHOR]

100 years ago, two scientists M.N. Saha and S.N. Basu tried to give an equation of state for real gas system by taking into consideration the probabilistic theory of finite volume of gas molecules as well as the influence of cohesive force. As compared to experimental observation, their theoretical prediction elucidates very close agreement of critical coefficient value. However, this unusual equation of state gets very little attention from the scientific community. In this study, the Saha-Basu equation is revisited. Critical coefficients as well as critical exponents corresponding to Saha-Basu equation are critically explored. Furthermore, interactions among the gas particles obeying Saha-Basu equation is still an open problem which we try to discuss in this article. [ABSTRACT FROM AUTHOR]

We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis. Our model may be helpful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates D A and D B , for the classes A and B, respectively, and obeying three diffusive regimes, i.e., D A < D B , D A = D B , and D A > D B . Into the same site i, the reaction occurs according to the dynamical rule based on Gillespie's algorithm. Finite-size scaling analysis has shown that our model exhibits continuous phase transition to an absorbing state with a set of critical exponents given by β / ν = 0.66 (1) , 1 / ν = 0.46 (2) , and γ ′ / ν = - 0.24 (2) familiar to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the mean-field universality class in both regular lattices and complex networks. [ABSTRACT FROM AUTHOR]

The critical behavior and its relation to the magnetocaloric effect in the amorphous Eu80Au20 alloy prepared by the melt-quenching technique are studied in detail. At 4.2 K, the magnetic moment is found to be 6.6 µB/Eu2+ ion (at µ0H = 4 T), which is smaller than the theoretical value of 7 µB/Eu2+ ion, indicating a misalignment of moments. The Curie-Weiss temperature (θP) and experimental effective magnetic moment μ eff exp are deduced from the Curie-Weiss law. The magnetic transition from the ferromagnetic state to the paramagnetic state was found to be a second-order magnetic phase transition. The critical exponents (CEs) in amorphous Eu80Au20 alloy are explored around its Curie temperature (TC) and are examined using a variety of techniques, including the modified Arrott plot, the Widom scaling relation, critical isotherm analysis, and the Kouvel-Fisher method. The computed values of the CEs agreed with those predicted by the mean-field approach. Based on these results, one may be able to conclude that the ferromagnetic exchange interaction is the long-range type. [ABSTRACT FROM AUTHOR]

There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards–Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time T ∗ that separates the dynamics into two distinct regimes: for T > T ∗ , we observe the typical behavior of pinned surfaces, while for T < T ∗ , the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ( H < 0.5 ) and correlated ( H > 0.5 ) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent θ to increase monotonically with H. [ABSTRACT FROM AUTHOR]

We investigate the nature of quantum criticality and topological phase transitions near the critical lines obtained for the extended Kitaev chain with next nearest neighbor hopping parameters and non-Hermitian chemical potential. We surprisingly find multiple gap-less points, the locations of which in the momentum space can change along the critical line unlike the Hermitian counterpart. The interesting simultaneous occurrences of vanishing and sign flipping behavior by real and imaginary components, respectively of the lowest excitation is observed near the topological phase transition. Introduction of non-Hermitian factor leads to an isolated critical point instead of a critical line and hence, reduced number of multi-critical points as compared to the Hermitian case. The critical exponents obtained for the multi-critical and critical points show a very distinct behavior from the Hermitian case. [ABSTRACT FROM AUTHOR]

Computer simulation of the three-component Potts model on a hexagonal lattice was carried out using the Monte Carlo method. Systems with linear dimensions L × L = N, L = 20–320 in units of interatomic distances are considered. Based on the theory of finite-size scaling, the static critical exponents of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated. The data we obtained confirm that in the considered Potts model on a hexagonal lattice, a second-order phase transition is observed with critical exponents corresponding to the universality class of the three-component Potts model. [ABSTRACT FROM AUTHOR]

Double-layered LaBiCaMn2O7 perovskites were synthesized using solid-state reaction. The critical exponents were explored around its Curie temperature. The magnetic transition nature from ferromagnetic to paramagnetic states was found to be a second-order. Several methods, including the modified Arrott plot technique (MAP), the Widom scaling relation (WSR), the critical isotherm analysis (CIA), and the Kouvel-Fisher (KF), were used to examine the critical exponents. A different investigation of the critical behaviour by the use of the magnetocaloric effect was also presented. We demonstrate that it is in accordance with the investigation of the magnetization data. The values of the critical exponents (CEs) computed were consistent with those predicted by the mean field approach. On the basis of these results, one may be able to conclude that the ferromagnetic exchange interaction is a long-range order. [ABSTRACT FROM AUTHOR]

The Cauchy problem for a model nonlinear equation with gradient nonlinearity is considered. We prove the existence of two critical exponents, and , such that this problem has no local-in-time weak (in some sense) solution for , while such a solution exists for , but, for , there is no global-in-time weak solution. [ABSTRACT FROM AUTHOR]

In this paper, by using variational methods we investigate the existence of solutions for the following system of elliptic equations - Δ g u + a (x) u + b (x) v = α 2 ∗ f (x) u | u | α - 2 | v | β in M , - Δ g v + b (x) u + c (x) v = β 2 ∗ f (x) v | v | β - 2 | u | α in M , where (M, g) is a smooth closed Riemannian manifold of dimension n ≥ 3 , Δ g is the Laplace–Beltrami operator, a, b and c are functions Hölder continuous in M, f is a smooth function and α > 1 , β > 1 are two real numbers such that α + β = 2 ∗ , where 2 ∗ = 2 n / (n - 2) denotes the critical Sobolev exponent. We get these results by assuming sufficient conditions on the function h = α 2 ∗ a + 2 α β 2 ∗ b + β 2 ∗ c related to the linear geometric potential n - 2 4 (n - 1) R g , where R g is the scalar curvature associated to the metric g. [ABSTRACT FROM AUTHOR]

This paper concerns the Cauchy problem for the nonlinear Schrödinger equation with power nonlinearity. Time local well-posedness in H s (R N) is proved in the case where the nonlinear term is critical from the scaling point of view, and has limited regularity so that the nonlinear term does not belong to C s (R 2 ; R 2) . [ABSTRACT FROM AUTHOR]

We study the following nonlinear critical elliptic equation - Δ u + ϵ Q (y) u = u N + 2 N - 2 , u > 0 in R N , where ϵ > 0 is small and N ≥ 5. Assuming that Q(y) is periodic in y 1 with period 1 and has a local minimum at 0 satisfying Q (0) > 0 , we prove the existence and local uniqueness of infinitely many bubbling solutions of it. This local uniqueness result implies that some bubbling solutions preserve the symmetry of the potential function Q(y), i.e., the bubbling solution whose blow-up set is { (j L , 0 , … , 0) : j = 0 , ± 1 , ± 2 , … , ± m } must be periodic in y 1 provided that ϵ goes to zero and L is any positive integer, where m is the number of the bubbles which is large enough but independent of ϵ. [ABSTRACT FROM AUTHOR]

Open quantum systems have been shown to host a plethora of exotic dynamical phases. Measurement-induced entanglement phase transitions in monitored quantum systems are a striking example of this phenomena. However, naive realizations of such phase transitions requires an exponential number of repetitions of the experiment which is practically unfeasible on large systems. Recently, it has been proposed that these phase transitions can be probed locally via entangling reference qubits and studying their purification dynamics. In this work, we leverage modern machine learning tools to devise a neural network decoder to determine the state of the reference qubits conditioned on the measurement outcomes. We show that the entanglement phase transition manifests itself as a stark change in the learnability of the decoder function. We study the complexity and scalability of this approach in both Clifford and Haar random circuits and discuss how it can be utilized to detect entanglement phase transitions in generic experiments. Measurement-induced phase transitions are notoriously difficult to observe. Here, the authors propose a neural-network-based method to map measurement outcomes to the state of reference qubits, allowing observation of the transition and extracting its critical exponents. [ABSTRACT FROM AUTHOR]

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-Tc superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi2−zPbzSr2−yLayCuO6+x. The ratio of the phase correlation length ξCDW to the orientation correlation length ξorient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range. Charge order has been widely observed in cuprate superconductors. Here, the authors conduct scanning tunneling microscopy measurements on (BiPb)2(SrLa)2CuO6+x and find that the charge order fills the bulk and is predominantly unidirectional with classical, rather than quantum, critical fluctuations. [ABSTRACT FROM AUTHOR]

Physically relevant field-theoretic quantities are usually derived from perturbation techniques. These quantities are solved in the form of an asymptotic series in powers of small perturbation parameters related to the physical system, and calculating higher powers typically results in a higher amount of computational complexity. Such divergent expansions were handled using hypergeometric functions, continued functions, and Borel–Leroy transforms. Hypergeometric functions are expanded as series, and a rough estimate of next-order information is predicted using information from known orders. Continued functions are used for the resummation of these series. The effective nature of extrapolation using such functions is illustrated by taking different examples in field theories. In the vicinity of second-order phase transitions, critical exponents are the most interesting numerical quantities corresponding to a wide range of physical systems. Using the techniques mentioned in this work, precise estimates are obtained for these critical exponents in ϕ 4 and ϕ 3 field models. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the critical behavior at the paramagnetic ferromagnetic (PM-FM) phase transition (PT) in GdTbHoErLa (GTHEL) alloy. Near the PM-FM PT, the usefulness of the Landau theory leads to generate isothermal magnetizations M (H , T) . Through an iterative program based on the Kouvel–Fisher method, the critical exponents have been optimized. They were found to be γ = 1.04 and β = 0.82 . Thus, the exponent at the Curie temperature δ was estimated to be 2.27 . Moreover, the critical parameters are unambiguous and reasonable, but they are not matching with the conventional universality classes. [ABSTRACT FROM AUTHOR]

The paper is concerned with the p-Laplacian minimizing problem with critical Stein–Weiss type term, and a nonlocal nonlinear equation involving fractional p-Laplacian operator and critical Stein–Weiss type term. Then main difficulty is hard to get the compactness of bounded minimizing sequence (and bounded Palais–Smale sequence). By the refined Sobolev inequality with Lorentz norm, we establish a abstract theorem, which is the relatively compactness result of bounded symmetric decreasing sequence. And then, as applications, we prove the existence, decay and regular results for the problems. [ABSTRACT FROM AUTHOR]

We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent close to 1. [ABSTRACT FROM AUTHOR]

Magnetization measurements have been carried out to study the behavior of isothermal magnetic entropy change and critical magnetic equation of state of EuS. X-ray diffraction data exhibits rock salt-type cubic structure of EuS. Magnetization measurements indicate a ferromagnetic to paramagnetic phase transition at TC ~ 16.8 K. Isothermal magnetic entropy change exhibits nonmonotonic behavior with temperature exhibiting a peak around TC. The peak value systematically increases with the increase of field change ΔH and the peak value, ΔSmax is ~ 45 J/kg K for ΔH of 70 kOe. Arrott plots and superposition of normalized entropy change graphs for different ΔH with respect to rescaled temperature θ indicate the phase transition to be of second-order type. The temperature variation of exponent n of exponential variation of ΔS with ΔH shows nonmonotonic behavior displaying the minimum at TC for n ~ 0.57. The magnetic critical exponents for the system are found to be β = 0.30, γ = 1.32, and δ = 5.32. Furthermore, analysis reveals that long-range exchange interaction is not supported in this system. Deviation of the critical exponents from the isotropic short-range Heisenberg exchange model in this system is surmised due to magnetic anisotropy and dipolar interactions. [ABSTRACT FROM AUTHOR]