Magnetic Exponents Research Articles

Complex magnetic interactions and critical behavior analysis in quaternary CoFeV0.8Mn0.2Si Heusler alloy

We investigate the magnetic behavior and critical exponents of quaternary CoFeV0.8Mn0.2Si Heusler alloy to understand the interactions across the Curie temperature (TC). The Rietveld refinement of the x-ray diffraction pattern with the space group F4¯3m confirms a single-phase cubic Y-type crystal structure. The magnetic susceptibility χ(T) data show a ferromagnetic nature with a second-order phase transition from paramagnetic to ferromagnetic at 446±1 K. The saturation magnetization at 5 K is found to be 2.2 μB/f.u., which is close to the Slater–Pauling rule and indicates its half-metallic nature. The values of asymptotic critical exponents (β, γ, and δ) and the TC are extracted through detailed analytical analysis including the modified Arrott plot, the Kouvel–Fisher (K–F) method, and the Widom scaling relation. Interestingly, the estimated values of β=0.369 and γ=1.445 closely approximate the theoretical values of the 3D Heisenberg model across the TC and validate the second-order thermodynamic phase transition. The obtained exponents lead to the collapse of renormalized isotherms, represented by the relationship between the magnetization (m) and the applied magnetic field (h), into two distinct branches above and below the TC, which validates the reliability of the analysis. Furthermore, these exponents suggest that the spin interaction follows a decay pattern of J(r)∼r−4.99, indicating a short-range magnetic ordering, akin to the itinerant-electron 3D Heisenberg model.

Theoretical determination of Ising-type transition by using the Self-Consistent Harmonic Approximation

Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been successfully utilized to determine the transition temperature of many different magnetic models, particularly the Berezinskii–Thouless–Kosterlitz transition in two-dimensional ferromagnets. More recently, the SCHA has found application in describing ferromagnetic samples in spintronic experiments. In such a case, the SCHA has proven to be an efficient formalism for representing the coherent state in the ferromagnetic resonance state. One of the main advantages of using the SCHA is the quadratic Hamiltonian, which incorporates thermal spin fluctuations through renormalization parameters, keeping the description simple while providing excellent agreement with experimental data. In this article, we investigate the SCHA application in easy-axis magnetic models, a subject that has not been adequately explored to date. We obtain both semiclassical and quantum approaches of the SCHA for a general anisotropic magnetic model and employ them to determine various quantities such as the transition temperature, spin-wave energy spectrum, magnetization, and critical exponents. To verify the accuracy of the method, we compare the SCHA results with experimental and Monte Carlo simulation data for many distinct well-known magnetic materials.

Existence of ground states for fractional Choquard–Kirchhoff equations with magnetic fields and critical exponents

Existence of ground states for fractional Choquard–Kirchhoff equations with magnetic fields and critical exponents

Optimal classification and similarity solution for unsteady flow behind a shock wave in a perfectly conducting dusty gas with magnetic field using group invariance method

We have studied the one dimensional unsteady isothermal and adiabatic flows behind the shock waves in a non-ideal dusty gas under the effect of magnetic field using Lie group invariance method. This method is used to get the infinitesimal generators of the Lie algebra. The concept of optimal systems is used for minimizing the group-invariant solutions. The optimal system of subalgebra is used to obtain the similarity variables and similarity transformation which transform the set of partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). Consequently, the system of ODEs in different cases is solved by using Runge–Kutta (R-K) method of forth order to derive the similarity solution in the cases of isothermal and adiabatic flows. The detailed discussions are illustrated by graph through numerical calculation in the case of power-law shock path. It is shown that the shock wave strength has decaying effects with an increase in the values of Alfven Mach number, adiabatic exponent of the gas, and gas non-idealness parameter. Also, the shock strength increases with an increment in the values of mass concentration of solid particles, magnetic field variation exponent, the ratio of density of solid particles to the gas initial density, and by changing the geometry from cylindrical to spherical.

Magnetic, magnetocaloric and critical exponent properties of Eu3(PO4)2 prepared by sol gel method

The Eu3(PO4)2 compound was prepared by the sol gel chemical route and its magnetic, magnetocaloric, and critical exponent properties have been investigated. Combining different models, a detailed analysis of the magnetic phase transitions in the Eu3(PO4)2 compound has been actually performed. At 5.9 K, the phase transition from the AFM (Antiferromagnetic) state to the PM (Paramagnetic) state is 2nd order. A phenomenological model is now used to comprehend the MCE (magnetocaloric effect) behavior of this sample. The CEs (Critical Exponents) are clearly obtained employing MAPs (Modified-Arrott-Plots), CIA (Critical Isotherm Analysis) and also WSR (Windom Scaling Relation) techniques based upon the data of magnetic measurements registered around the TN (Néel temperature). Besides, an analysis of critical performance on the basis of the MCE is also provided. These exponents are β (beta), γ (gamma), and δ (delta) were properly revealed to be nearby those of the MFM (Mean-Field-Model) values. This simply reflects the existence of an AFM long-range order in our sample. A single equation of state also can be used to scale the magnetization below and above TN. Nevertheless, it should be noted that the scaling relations are respected, which indicates a renormalization of the interactions nearby the TN. The forecasting of the J(r) (exchange interaction) validated the long-range AFM order in this sample.

Influence of Thermophoresis and Brownian Motion of Nanoparticles on Radiative Chemically-Reacting MHD Hiemenz Flow over a Nonlinear Stretching Sheet with Heat Generation

In this study, a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered. Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations (ODEs), the implications of heat generation, and chemical reaction on the flow field are described in detail. Moreover a Homotopy analysis method (HAM) is used to interpret the related mechanisms. It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity, while thermophoresis and Brownian motion promote specific thermal effects. The results also demonstrate that as the Brownian motion parameter is increased, the concentration values become smaller.

Theoretical aspects of magnetic, magnetocaloric, and critical exponents: Nanomaterial model

In this present research paper, our focus was on studying the nanomaterial model with the spin vector and its amplitude was 5/2: the magnetic, magnetocaloric effect and the critical exponents. By using Monte Carlo method, I succeeded in determining the fact that the magnetic transition nature was second-order with the Curie temperature of TC = 14.46 K. The maximum magnetic entropy change (of) (ΔSM) of 3.53 J kg-1K−1, the large Relative Cooling Power (RCP) of 32.67 J kg−1 and the corresponding maximum Refrigeration Capacity (RC) of 24.50 J kg−1 were established under the magnetic field of 8 T. The critical exponents were determined with the purpose of studying the nature and underlying mechanism of the Ferromagnetic (FM) to the Paramagnetic (PM) phase transition. The critical exponents were obtained using magnetocaloric data from the field dependence of the magnetic entropy, the relative cooling power and Widom scaling relation. β, γ and δ indicated that the nanomaterial model belonged to the two-dimensional (2D)-Ising model with long-range interaction.

Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge

There has been much recent progress on exotic surface critical behavior, yet the classical-quantum correspondence of special and extraordinary-log criticality remains largely unclear. Employing worm Monte Carlo simulations, we explore the surface criticality at an emergent superfluid-Mott insulator critical point in the Villain representation, which is believed to connect classical and quantum O(2) critical systems. We observe a special transition with the thermal and magnetic renormalization exponents $y_t=0.58(1)$ and $y_h=1.690(1)$ respectively, which are close to recent estimates from models with discrete spin variables. The existence of extraordinary-log universality is evidenced by the critical exponent $\hat{q}=0.58(2)$ from two-point correlation and the renormalization-group parameter $\alpha=0.28(1)$ from superfluid stiffness, which obey the scaling relation of extraordinary-log critical theory and recover the logarithmic finite-size scaling of critical superfluid stiffness in open-edge quantum Bose-Hubbard model. Our results bridge recent observations of surface critical behavior in the classical statistical mechanical models [Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021); Hu $et$ $al.$, $ibid.$ 127, 120603 (2021); Parisen Toldin $et$ $al.$, $ibid.$ 128, 215701 (2022)] and the open-edge quantum Bose-Hubbard model [Sun $et$ $al.$, Phys. Rev. B 106, 224502 (2022)].

Magneto-Hydrodynamic Flow above Exponentially Stretchable Surface with Chemical Reaction

This article is focused on investigating the convective magneto-hydrodynamic single-phase flow for comparative analysis of two different base fluids above an exponentially stretchable porous surface under the effect of the chemical reaction. The Buongiorno fluid model is incorporated to observe the Thermophoresis and Brownian diffusion in this study. Boussinesq approximation for temperature and concentration are accounted for flow to be naturally convective. In this study, water and ethanol are assumed for comparative analysis. Additionally, to achieve the outcomes of the designed three-dimensional flow boundary value, problem technique is employed to simulate the problem in MATLAB. Increase in the magnetic field, thermophoresis diffusion, temperature exponent, and Prandtl number expand thermal boundary, whereas contraction is observed with an increase in porosity. Shear stress rates in respective directions have decreased with an increase in the stretching ratio of the surface. Moreover, through comparison, reasonably enhanced Nusselt number is observed for water under influence of study parameters while the Nusselt number abruptly decreases for ethanol. High mass coefficients are observed for both examined fluids.

Magnetic susceptibility of the square lattice Ising model

In this work, we obtained an analytical relation for the susceptibility of the square lattice Ising model. Our investigation is based on an average magnetization interrelation which was recently obtained by us. To proceed further, we have to make a mathematical conjecture about the three-site correlation function appearing in the average magnetization interrelation. We presented the conjectured mathematical form of the three spin correlation function with the relation, \(\langle \sigma _{1}\sigma _{2}\sigma _{3}\rangle =a(K,H)\langle \sigma \rangle +[1-a(K,H)]\langle \sigma \rangle ^{(1+\beta ^{-1})}\). Here, \(\beta\) denotes the critical exponent for the average magnetization and a(K, H) is a function whose behavior will be described around the critical point with an arbitrary constant. To elucidate the relevance of the method, we have first calculated the susceptibility of the 1D chain as an example, and the obtained susceptibility expression for the 1D chain is equivalent to the result of the susceptibility obtained by the conventional method. Applying the same method, we obtained the values of the magnetic critical exponent \(\gamma\) of the square lattice Ising model. The values of \(\gamma\) are obtained as \(\gamma =1.72\) for \(T\!>\!T_{c}\), and \(\gamma =0.91\) for \(T\!<\!T_{c}\).

Ground states for fractional Choquard equations with magnetic fields and critical exponents

Abstract In this paper, we investigate the ground states for the following fractional Choquard equation with magnetic fields and critical exponents: ( - Δ ) A s ⁢ u + V ⁢ ( x ) ⁢ u = λ ⁢ f ⁢ ( x , u ) + [ | x | - α ∗ | u | 2 α , s * ] ⁢ | u | 2 α , s * - 2 ⁢ u in ⁢ ℝ N , (-\Delta)_{A}^{s}u+V(x)u=\lambda f(x,u)+[\lvert x\rvert^{-\alpha}\ast\lvert u% \rvert^{2^{*}_{\alpha,s}}]\lvert u\rvert^{2^{*}_{\alpha,s}-2}u\quad\text{in }% \mathbb{R}^{N}, where λ &gt; 0 {\lambda&gt;0} , α ∈ ( 0 , 2 ⁢ s ) {\alpha\in(0,2s)} , N &gt; 2 ⁢ s {N&gt;2s} , u : ℝ N → ℂ {u:\mathbb{R}^{N}\rightarrow\mathbb{C}} is a complex-valued function, 2 α , s * = ( 2 ⁢ N - α ) / ( N - 2 ⁢ s ) {2^{*}_{\alpha,s}=(2N-\alpha)/(N-2s)} is the fractional Hardy–Littlewood–Sobolev critical exponent, V ∈ ( ℝ N , ℝ ) {V\in(\mathbb{R}^{N},\mathbb{R})} is an electric potential, V and f are asymptotically periodic in x, A ∈ ( ℝ N , ℝ N ) {A\in(\mathbb{R}^{N},\mathbb{R}^{N})} is a magnetic potential, and ( - Δ ) A s {(-\Delta)^{s}_{A}} is a fractional magnetic Laplacian operator with s ∈ ( 0 , 1 ) {s\in(0,1)} . We prove that the equation has a ground state solution for large λ by using the Nehari method and the concentration-compactness principle.

Semiconducting nature, magnetic critical exponent, and magnetocaloric effect study near room temperature on Fe[sbnd]Mn[sbnd]Al alloy

The Fe2.5Mn0.5Al Heusler alloy, prepared by Arc melting method, crystallizes to B2 in the Fm-3m space group. Resistivity measurement shows semi-metallic behavior in low temperature due to the dominance of magnon-magnon scattering and, exhibits semiconducting nature above the Curie temperature. Hence, it is predicted that there is a correlation between magnetic ordering and electrical transport properties. Arrott plot, Kouvel fisher method, and Widom scaling relation have been used here to determine the critical exponents. The Curie temperature (TC) is found to be near room temperature at 280 K. Also, critical exponents indicate that the magnetic ordering is following mean-field theory i.e., long-range interaction is present with 2nd order para to ferromagnetic transition. On the other hand, due to the 2nd order magnetic phase transition, significant magnetocaloric effect has been observed in a wide temperature range near room temperature. The maximum entropy change is found at 280 K i.e., at Tc.

Critical behavior of the Ashkin–Teller model with a line defect: Towards reconciliation between numerical and analytical results

We study magnetic critical behavior in the two-dimensional Ashkin–Teller model with an asymmetric defect line. This system is represented by two Ising lattices of spins σ and τ interacting through a four-spin coupling ε. In addition, the couplings between σ-spins are modified along a particular line, whereas couplings between τ-spins are kept unaltered. This problem has been previously considered by means of analytical field-theoretical methods and by numerical techniques, with contradictory results. For ε>0 field-theoretical calculations give a magnetic critical exponent corresponding to σ-spins which depends on the defect strength only (it is independent of ε), while τ-spins magnetization decay with the universal Ising value 1/8. On the contrary, numerical computations based on density matrix renormalization (DMRG) give, for ε>0 similar scaling behaviors for σ and τ spins, which depend on both ε and defect intensity. In this paper we revisit the problem by performing a direct Monte Carlo simulation. Our results are in good agreement with DMRG computations. By reexamining the field-theoretical approach, we show how numerical and analytical results can be reconciled when a more general regularization prescription is adopted.

Random Crystal Field Effect on the Critical Properties of the Mixed Spin-(52,12) Anisotropic Heisenberg Model in the Oguchi Approximation

We have employed the Oguchi approximation (OA) to investigate the effects of a random crystal field which is active (inactive) with probability [Formula: see text] [Formula: see text] for given lattice sites on the thermodynamic properties of the mixed spin-[Formula: see text] anisotropic Heisenberg model in the presence of an external magnetic field. By exploiting the thermal variations of the order parameters, interesting phase diagrams are produced on various planes. The phase diagrams show first- and second-order transition lines and also tricritical points. In addition to the reentrant behavior which is localized in a certain range of [Formula: see text] at very low temperature, the magnetic exponent [Formula: see text] calculated near the critical point exhibits interesting behaviors depending on the crystal field interaction. The hysteresis behavior of the model is also investigated and it reveals that the width of hysteresis loop decreases or increases, respectively, for negative or positive crystal field region as the probability [Formula: see text] increases.

Phase transitions in a three-dimensional Ising model with cluster weight studied by Monte Carlo simulations.

The loop model is an important model of statistical mechanics and has been extensively studied in two-dimensional lattices. However, it is still difficult to simulate the loop model directly in three-dimensional lattices, especially in lattices with coordination numbers larger than 3. In this paper, a cluster weight Ising model is proposed by introducing an additional cluster weight n in the partition function of the traditional Ising model. This model is equivalent to the loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. By using a Monte Carlo method with cluster updates and color assignment, we obtain the global phase diagram containing the paramagnetic and ferromagnetic phases. The phase transition between the two phases is second order at 1≤n<n_{cri} and first order at n≥n_{cri}, where n_{cri}≈2. The thermal exponent y_{t} is equal to the system dimension d when the first-order transition occurs. For the second-order transitions, the numerical estimation of y_{t} and the magnetic exponent y_{m}, shows that the universalities of the two models on the three-dimensional lattice are different. Our results are helpful in the understanding of some traditional statistical mechanics models.

Clock model interpolation and symmetry breaking in O(2) models

Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model by adding a $\gamma \cos(q\varphi)$ term to the ordinary O(2) model with angular values restricted to a $2\pi$ interval. In the $\gamma \rightarrow \infty$ limit, the model becomes an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuation of the clock model for noninteger $q$. By shifting the $2\pi$ integration interval, the number of angles selected can change discontinuously and two cases need to be considered. What we call case $1$ has one more angle than what we call case $2$. We investigate this class of clock models in two space-time dimensions using Monte Carlo and tensor renormalization group methods. Both the specific heat and the magnetic susceptibility show a double-peak structure for fractional $q$. In case $1$, the small-$\beta$ peak is associated with a crossover, and the large-$\beta$ peak is associated with an Ising critical point, while both peaks are crossovers in case $2$. When $q$ is close to an integer by an amount $\Delta q$ and the system is close to the small-$\beta$ Berezinskii-Kosterlitz-Thouless transition, the system has a magnetic susceptibility that scales as $\sim 1 / (\Delta q)^{1 - 1/\delta'}$ with $\delta'$ estimates consistent with the magnetic critical exponent $\delta = 15$. The crossover peak and the Ising critical point move to Berezinskii-Kosterlitz-Thouless transition points with the same power-law scaling. A phase diagram for this model in the $(\beta, q)$ plane is sketched. These results are possibly relevant for configurable Rydberg-atom arrays where the interpolations among phases with discrete symmetries can be achieved by varying continuously the distances among atoms and the detuning frequency.

Random sampling neural network for quantum many-body problems

The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as the system size increases. A few numerical methods have been developed for some specific systems, but may not be applicable in others. Here we propose a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable 1D models, including Ising model with transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to test the applicability of RSNN. Pretty high accuracy of energy spectrum, magnetization and critical exponents etc. can be obtained within the strongly correlated regime or near the quantum phase transition point, even the corresponding RSNN models are trained in the weakly interacting regime. The required computation time scales linearly to the system size. Our results demonstrate that it is possible to combine the existing numerical methods for the training process and RSNN to explore quantum many-body problems in a much wider parameter regime, even for strongly correlated systems.

A self-similar solution for unsteady adiabatic and isothermal flows behind the shock wave in a non-ideal gas using Lie group analysis method with azimuthal or axial magnetic field in rotating medium

The similarity solutions using Lie group analysis for shock wave propagation in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field in the case of isothermal and adiabatic flows are obtained. All possible cases of similarity solutions are discussed using the Lie group analysis for the isothermal and adiabatic flows. The arbitrary constants involved in the generators of local Lie groups bring various possible cases of solutions with exponential law and power law shock paths. Similarity solution for isothermal and adiabatic flows with power law shock path is discussed in detail. The density of ambient medium is taken to be constant. The axial and azimuthal fluid velocities and magnetic field in the ambient medium are assumed to be varying according to power law. The effect on shock wave strength and that on the flow variables due to variation of the Alfven Mach number, adiabatic index of the gas, non-idealness parameter, rotational parameter and initial magnetic field variation exponent are investigated. It is found that these parameters have decaying effects on shock wave. The obtained results in the case of isothermal and adiabatic flows are also compared with each other.

Two‐dimensional thin layer convective flow with heat transfer from magneto‐hydrodynamic uniform free convection flow driven by nonlinear stretching surface

AbstractA uniform two‐dimensional magneto‐hydrodynamic convection flow of an adhesive incompressible fluid along a vertical stretching surface in accordance with varying thermal conductivity and radiation is analyzed. The uppermost layer temperature, the transverse magnetic field and the stretching velocity are presumed to alter as a power function of the distance from the origin. The non‐linear PDE (partial differential equations) which run our examined problem are converted into a set of non‐linear ordinary differential equations by the use of a relevant transformations followed by a numerical solution implementing a shooting method together with Runge‐Kutta integration formula. We examine the effects of a variety of regulating parameters, viz the magnetic parameter, the velocity and temperature exponents, the variable thermal conductivity parameter, buoyancy parameter and the radiation parameter. The graphs and tables express a powerful impact of these parameters on the behavior of the flow and heat transfer.

Thermomagnetic properties and critical behaviour studies in the ferromagnetic – Paramagnetic phase transition in Pr0.6Sr0.35Ag0.05MnO3 and Pr0.6Sr0.3Ag0.1MnO3 ceramics

Abstract Magnetic ordering and critical exponents of Pr0.6Sr0.35Ag0.05MnO3 (x = 0.05) and Pr0.6Sr0.3Ag0.1MnO3 (x = 0.1) ceramics are identified by magnetic measurements. Banerjee criterion and field dependences of the ΔSMmax disclose that both samples exhibit a second-order phase transition. The values obtained for the magnetic performances make these samples promising candidates for magnetic refrigeration. The determined exponents obey the mean-field model with a long-range ferromagnetic interaction. The reliability of the obtained critical exponents is examined by using the universal scaling hypothesis. Temperature variation in effective exponents βeff and γeff resemble with those for disordered ferromagnet. Using critical exponents universal curves for the ΔSM(T) are constructed.