Critical Exponents Research Articles

Deciphering the Roots of Pharmacists’ Critical Thinking About Pseudoscientific Claims: Insights from a Cross-Sectional Survey

The global trend toward self-medication has increased public reliance on over-the-counter treatments and health-related information, contributing to the spread of pseudoscientific claims in healthcare and posing serious public health risks. Pharmacists, as accessible healthcare professionals, play a crucial role in critically evaluating these claims and providing evidence-based guidance. However, little quantitative research has assessed pharmacists’ critical thinking regarding pseudoscientific claims or the factors influencing them. This study aims to evaluate the demographic factors affecting pharmacists’ critical thinking about pseudoscientific claims. A cross-sectional survey was conducted among pharmacists in hospitals, insurance pharmacies, and drugstores across Japan. The newly developed Pseudoscience Criticism Scale (PCS) measured attitudes toward pseudoscientific claims. Statistical analysis identified factors that form and influence critical thinking. This study revealed two primary dimensions: “Medical Superstitions and Unscientific Treatments” and “Natural Healing Superstitions”. Gender and educational background significantly impacted PCS scores, with male pharmacists and graduates from six-year pharmacy programs exhibiting higher skepticism. These findings underscore the importance of ongoing professional development in pharmacy education to strengthen critical thinking. The PCS is an effective tool for assessing this competency. Enhancing educational efforts is essential to equip pharmacists to effectively counter pseudoscientific claims and improve public health.

Criticality-enhanced precision in phase thermometry

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study noninvasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behavior of finite many-body systems beyond the validity of mean-field models. Published by the American Physical Society 2024

Expansion of Landau theory with Magnetic Susceptibility and Heat Capacity

Abstract. Landau theory employs free energy to depict the work potential of molecules and utilizes order parameters to signify the degree of molecular organization. By applying a Taylor expansion of the free energy with respect to the order parameter in the vicinity of a phase transition, the theory elucidates how molecular arrangements can influence the system's energy. The universality of Landau theory stems from the order parameter within the framework of free energy expansion. The application of critical exponents exemplifies the universality of Landau theory, showcasing the properties of materials that share the same dimensionality and similar correlation lengths. This article aims to derive formulas and discuss practical applications of Landau theory, such as analyzing the heat capacity and magnetic susceptibility of materials across a range of temperatures.

Complex hyperbolic Kleinian groups of large critical exponents

Complex hyperbolic Kleinian groups of large critical exponents

Global Well-Posedness and Refined Regularity Criterion for the Uni-Directional Euler-Alignment System

Abstract We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi (x) = |x|^{-(d+\alpha )}$ for $\alpha \in (0,2)$. Our paper establishes global regularity results in both the subcritical regime $1<\alpha <2$ and the critical regime $\alpha =1$. Notably, when $\alpha =1$, the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime $0<\alpha <1$.

Bosonization and correlators of the one-dimensional Hubbard model

Abstract We present a simple derivation of the Luttinger liquid relation for the one-dimensional Hubbard model, considering a finite U and in the U = ∞ limit. We describe a simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and physical way using the bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary U through a single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and physically transparent way.

Relation between critical exponent of the conductivity and the morphological exponents of percolation theory

Relation between critical exponent of the conductivity and the morphological exponents of percolation theory

Phase transition of modified thermodynamics of the Kerr-AdS black hole

Abstract We investigate the critical phenomena of Kerr-AdS black holes in the modified first law of thermodynamics.
The modified black hole thermodynamics exhibits the van der Waals-like phase
structure. All the critical exponents are calculated, and the swallowtail diagram of free energy is
plotted. Comparing with existing results, the main difference is the correspondence between thermal
quantities of the Kerr-AdS black holes and the van der Waals system. In previous work[16],
the correspondence was $(\Omega_H, J)\to (V, P)$. In our work, the correspondence is $(J, {\hat\Omega}_H)\to (V, P)$.
This difference results from rotating effect. The modified black hole thermodynamics is associated
with rotating observers. The free energy in such reference contains an extra rotating energy. This
extra part induces a Legendre transformation in $({\hat\Omega}_H, J)$ cross-section, which yields the different
correspondence.

Criticality of global monopole charges in diverse dimensions

In this work, we construct charged AdS black holes with a global monopole charge in diverse dimensions and study the thermodynamics. We find a critical monopole charge below which the solution exhibits Van-der Waals like behaviors. In the context of holography, this could be interpreted using the boundary degrees of freedoms. As an example, we study the phase diagram in the four dimensions analytically. We further analyze the microstructures of the solution using Ruppeiner geometry. We find that repulsive interactions dominates for black holes in a wide range of temperatures. However, around the critical point, attractive interactions is dominant and the Ruppeiner scalar curvature shows universal behaviors: it has a critical exponent 2 and coefficient -1/8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-1/8$$\\end{document} in diverse dimensions. Universality of the results is interpreted from the scaling behavior of free energy near the critical point for Van-der Waals like fluids.

Temperature dependence of the frequency shifts related to the thermodynamic quantities close to phase transitions in NaNO2

ABSTRACT This study examines a linear relationship between the frequency shifts, ( 1 / w ) ( ∂w / ∂T ) p , and the variation of the dielectric constant, ( 1 / ϵ ) ( ∂ϵ / ∂T ) p , close to phase transitions in ferroelectric crystalline systems, in particular, ferroelectric NaNO2 as studied here. Both quantities (frequency and dielectric constant) are described by the power-law formulae below the Curie temperature Tc (ferroelectric phase), Tc < T < Ti (incommensurate phase) and T > Ti (paraelectric phase). The divergence behaviour of the mode Grüneisen parameter (ɣp ) is obtained, whose temperature dependence can also be described by a power-law formula in NaNO2. It is also shown that the heat capacity Cp can be evaluated from the thermal expansion (αp ) by means of the same critical exponent since they exhibit similar critical behaviour near Tc and Ti in this crystal.

Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

Longitudinal one-dimensional mechanical topological insulator

Abstract We present a study of a longitudinal one-dimensional mechanical topological insulator based on a slinky spring in the Su–Schrieffer–Heeger (SSH) configuration. The system demonstrates key characteristics of topological insulators, including the existence of edge states in the bandgap, exponential decay of amplitude, and a winding number of 1 for topological phases. By manipulating the stiffness of the spring through the placement of masses, we transition between trivial, metallic, and topological phases. Our findings also show that the edge states are robust against perturbations, and we observe a critical phase transition where the coherence length follows a critical exponent of -1, as predicted by theory. This simple mechanical system provides an accessible platform for studying the special properties of topological insulators and opens up new possibilities for exploring topological phenomena in classical systems.

Toward Postulating a Critical Digital Pedagogy Scale: Development and Validation of a Meta-Connective Attitude Questionnaire for the Online Classrooms

Although digital technology and democracy through digital learning environments are gaining attention in applied linguistics, the lack of a measurement scale with robust psychometric properties hinders progress towards education quality and learning opportunities. To address this gap, this study is a report on designing, constructing, and validating the practicality of critical digital pedagogy (CDP) scale. To undertake the study, a quantitative research following a survey design was adopted to (a) develop and validate the scale, and (b) to screen English as a foreign language (EFL) teachers’ perceptions. To gauge teachers’ perspectives, this study aimed to conceptualize the construct of CDP through the development and validation of a scale specifically designed for use in online classrooms. Utilizing both data-driven and theoretical approaches among 412 EFL teachers has resulted in the development of a 27-item CDP scale. Notably, the findings indicated a high level of internal consistency and satisfactory construct validity of the of the newly developed scale. Such scale can bridge the gap between critical pedagogy and digital instruction.

Fermionic Casimir energy in Horava–Lifshitz scenario

In this work, we investigate the violation of Lorentz symmetry through the Casimir effect, one of the most intriguing phenomena in modern physics. The Casimir effect, which represents a macroscopic quantum force between two neutral conducting surfaces, is widely regarded as a triumph of Quantum Field Theory. In this study, we present new results for the Casimir effect, focusing on the contribution of mass associated with fermionic quantum fields confined between two large parallel plates, in the context of Lorentz symmetry violation within the Horava–Lifshitz formalism. To calculate the Casimir energy and pressure, we impose a MIT bag boundary condition on the two plates, compatible with the higher-order derivative term in the modified Dirac equation. Our results reveal a strong influence of Lorentz violation on the Casimir effect. We observe that the Casimir energy is significantly affected, both in intensity and sign, potentially resulting in a repulsive or attractive force between the plates, depending on the critical exponent associated with the Horava–Lifshitz formalism.

Muon spin relaxation study of spin dynamics on a Kitaev honeycomb material H3LiIr2O6

The vacancy effect in quantum spin liquid (QSL) has been extensively studied. A finite density of random vacancies in the Kitaev model can lead to a pileup of low-energy density of states (DOS), which is generally experimentally determined by a scaling behavior of thermodynamic or magnetization quantities. Here, we report detailed muon spin relaxation (μSR) results of H3LiIr2O6, a Kitaev QSL candidate with vacancies. The absence of magnetic order is confirmed down to 80 mK, and the spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field (LF)-μSR polarization is observed down to 0.1 K. This indicates a dynamical scaling, whose critical exponent of 0.46 is excellently consistent with the scaling behavior of specific heat and magnetization data. All the observations point to the finite DOS with the form N(E)∼E−ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N(E)\\sim {E}^{-\ u }$$\\end{document}, which is expected for the Kitaev QSL in the presence of vacancies. Our μSR study provides a dynamical fingerprint of the power-law low-energy DOS and introduces a crucial new insight into the vacancy effect in QSL.

Multiple Solutions for a Critical Steklov Kirchhoff Equation

In the present work, we study some existing results related to a new class of Steklov p(x)-Kirchhoff problems with critical exponents. More precisely, we propose and prove some properties of the associated energy functional. In the first existence result, we use the mountain pass theorem to prove that the energy functional admits a critical point, which is a weak solution for such a problem. In the second main result, we use a symmetric version of the mountain pass theorem to prove that the investigated problem has an infinite number of solutions. Finally, in the third existence result, we use a critical point theorem proposed by Kajikiya to prove the existence of a sequence of solutions that tend to zero.

Investigation of geochemically induced permeability alteration in geothermal reservoirs and its implications for sustainable geothermal energy production

Geothermal resources constitute a significant portion of the world's low-carbon, renewable energy potential, with about 75% classified as low-temperature. One such potential resource exists in Precambrian basement rocks underlying the Williston Basin in southern Saskatchewan, Canada, with a reservoir temperature of 120 °C. However, geochemically induced permeability alteration in these highly reactive low-temperature granitoid resources poses a significant risk to long-term heat production. To assess and potentially mitigate this risk, we conducted a geochemical and mineralogical study of both altered and unaltered samples. Our findings facilitated the parameterization of geochemical simulations of water-rock interactions to predict mineral volume changes and, by extension, draw inferences on porosity and permeability changes resulting from these interactions. The simulations indicate an increased mineral volume in both samples, yet geothermal alteration of the unaltered, and thus more reactive, rocks induced relative mineral volume changes about 30% greater than those in the altered rocks. The resulting absolute change in porosity is 0.5 vol% for the unaltered rocks and 0.35 vol% for the altered rocks. Utilizing an empirical porosity-permeability relationship, the computed change in permeability indicates that the unaltered basement rock experienced a greater change in total permeability than the altered basement rocks. Additional calculations demonstrate the sensitivity of the porosity-permeability equation to critical porosity and power exponent, forecasting various scenarios with permeability changes ranging from 1.0 × 10−13 to 1 × 10−20 m2. Consequently, we infer that altered, permeable zones of the examined Precambrian basement rocks are likely to offer favourable conditions for sustained, multi-decade heat production, and thus should be targeted over less altered zones to justify initial capital expenditures. Globally, geothermal heat extraction from these rocks remains an underexplored yet promising resource for generating reliable, low-carbon renewable energy, crucial in our efforts to decarbonize the global economy.

The Impact of Epistemological Beliefs and School Climate on the Sustainability of Critical Thinking Dispositions in Middle School Students

The objective of this study is to ascertain whether school climate and students’ epistemological beliefs serve as predictors of sustainable critical thinking dispositions in middle school students. This research is designed as a correlational study. A total of 585 students from four middle schools in Çanakkale, Turkey, participated in the research. To this end, the researchers administered the Critical Thinking Disposition Scale, the Middle School Students’ Epistemological Belief Scale, and the School Climate Survey, gradually collecting the raw data. Following the collection of the data, they were subjected to analysis using multiple linear regression. The results of the statistical analysis demonstrated that the students’ critical thinking dispositions were significantly predicted by both epistemological beliefs and school climate. In other words, belief in the omniscient power of authority and quick learning were found to have a negative correlation with critical thinking, whereas belief in simple knowledge was observed to have an inverse positive relationship. The dimension of the school climate, relating to positive student–teacher relations, appeared to constitute a prospective positive predictor, while authoritarian student–teacher relations and the lack of resources were identified as the main negative classroom environment factors. The study highlights the complex mutual influence of individual beliefs and the learning environment in the development of critical thinking dispositions.

Anisotropic magnetic entropy change and magnetic critical behavior in van der Waals Fe3GaTe2

Fe3GaTe2, with intrinsic magnetism at ambient temperature and high perpendicular magnetic anisotropy, is a promising van der Waals material for 2D-materials-based spintronic devices. Herein, we report the anisotropic magnetocaloric effects and magnetic critical phenomena in Fe3GaTe2 single crystal. Owing to the large anisotropy, magnetic entropy change (−ΔSM) shows anisotropic character with −ΔSMmax of 1.67 J kg−1 K−1 along the c axis and 1.11 J kg−1 K−1 in the ab plane under field change of 5 T. The rotating ΔSM from the ab plane to the c axis reaches 0.67 J kg−1 K−1 at magnetic field of 5 T. By carefully fitting the −ΔSMmax and relative cooling power (RCP), we determine their relationships to be −ΔSMmax∝Hn (n = 0.694(1)) and RCP∝Hm (m = 1.301(3)) for the magnetic field along the c-axis. Further analysis of critical behavior near TC reveals critical exponents β = 0.41(1) at TC = 341.5(1) K, γ = 1.01(1) at TC = 341.6(3) K, and δ = 3.67(15) at TC = 340 K, indicating a three-dimensional complex magnetic exchange.

Sign-changing solutions for a class of fractional Choquard equation with the Sobolev critical exponent in [formula omitted]

In this paper, we study the following fractional Choquard equation with critical exponent(−Δ)σu+u=(Iα⁎|u|p)|u|p−2u+|u|2σ⁎−2uinR3, where σ∈(34,1), α∈(2σ,3) and α+2σ3−2σ<p<2α,σ⁎:=3+α3−2σ, 2α,σ⁎ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, 2σ⁎:=63−2σ is the fractional Sobolev critical exponent and the operator (−Δ)σ stands for the fractional Laplacian of order σ. Based on the above assumptions, we establish the existence of positive ground state solutions, and if p∈(α+2σ3−2σ,2α3−2σ), we also have the corresponding regular property. Subsequently, by introducing some other additional hypotheses on σ, α, p and with the help of quantitative deformation lemma, we employ constrained minimization arguments on the sign-changing Nehari manifold to obtain the existence of ground state sign-changing solutions.