Asymptotic Critical Region Research Articles

Quantum wetting transition in the cluster Ising model

The wetting transition in the one-dimensional cluster Ising model with opposite boundary fields is studied. Tuning one boundary field while fixing another leads to the occurrence of phase transitions, where the transition points depend on the cluster coupling. Furthermore, the phase diagram is divided into three regions with different phase transition. For weak and strong cluster coupling, the phase transition is continuous and belongs to the same universality of transverse Ising model with boundary fields. For intermediate cluster coupling, the phase transition is first order. In the strong cluster coupling region, the critical region becomes exponentially small and the asymptotic behavior is absent even for lattice size up to 104. A numerical method to solve the energy gap and the correlation length is proposed on an infinite long spin chain. With this method, one can get the critical behavior as close to the critical point as possible provided that the numerical accuracy is high enough. In the light of this method, we clearly show that there is a preasymptotic regime in which the apparent critical exponents depend on the cluster coupling. Moreover, we obtain the accurate energy gap exponent zν and the correlation length exponent ν in the asymptotic critical region.

Unraveling the magnetic properties and nature of exchange interactions of Mn5−x Fe x Ge3 (0.15 ≤ x ≤ 0.5) alloys

We report the structural and magnetic properties of arc-melted Fe-doped Mn5Ge3 alloys. In this study, Mn5−x Fe x Ge3 (x = 0.15, 0.3, and 0.5) alloys were subjected to DC magnetic measurements in order to examine the nature of magnetic interaction via critical exponents study in the asymptotic critical region. The critical exponents β, γ and δ are obtained independently from different methods. For Mn4.85Fe0.15Ge3, β = 0.338, γ = 1.146 and δ = 4.39; for Mn4.7Fe0.3Ge3, β = 0.337, γ = 1.244 and δ = 4.69 and for Mn4.5Fe0.5Ge3, β = 0.328, γ = 1.195 and δ = 4.64. The values of critical exponents obtained are found to be close to the 3D Ising universality class (β = 0.325, γ = 1.241, and δ = 4.82). Analyses based on the Renormalization group theory predictions reveal that the spin interactions are short-range extended types beyond the nearest neighbors due to the presence of a different set of Mn–Mn interactions with an unequal magnitude of exchange strengths in the Mn5−x Fe x Ge3 alloys.

Real-time detection of a change-point in a linear expectile model

In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the explanatory variables number is large. We build test statistics based on the cumulative sum (CUSUM) of the expectile function derivatives calculated on the residuals obtained by the expectile and adaptive LASSO expectile estimation methods. The asymptotic distribution of these statistics are obtained under the hypothesis that the model does not change. Moreover, we prove that they diverge when the model changes at an unknown observation. The asymptotic study of the test statistics under these two hypotheses allows us to find the asymptotic critical region and the stopping time, that is the observation where the model will change. The empirical performance is investigated by a comparative simulation study with other statistics of CUSUM type. Two examples on real data are also presented to demonstrate its interest in practice.

Phase boundary near a magnetic percolation transition

Motivated by recent experimental observations [Rowley et al. in Phys Rev 96:020407, 2017] on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close to the lattice percolation threshold. We perform large-scale Monte Carlo simulations of XY and Heisenberg models on both simple cubic lattices and lattices representing the crystal structure of the hexagonal ferrites. Close to the percolation threshold $$p_\mathrm{c}$$ , we find that the magnetic ordering temperature $$T_\mathrm{c}$$ depends on the dilution p via the power law $$T_\mathrm{c} \sim |p-p_\mathrm{c}|^\phi $$ with exponent $$\phi =1.09$$ , in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, $$|p-p_\mathrm{c}| \lesssim 0.04$$ . Outside of it, the shape of the phase boundary is well described, over a wide range of dilutions, by a nonuniversal power law with an exponent somewhat below unity. Nonetheless, the percolation scenario does not reproduce the experimentally observed relation $$T_\mathrm{c} \sim (x_\mathrm{c} -x)^{2/3}$$ in PbFe $$_{12-x}$$ Ga $$_x$$ O $$_{19}$$ . We discuss the generality of our findings as well as implications for the physics of diluted hexagonal ferrites.

Scaling study of magnetic phase transition and critical behavior in Nd0.55Sr0.45Mn0.98Ga0.02O3 manganite

Microscopic magnetic interactions and magnetism can be probed by studying the critical paramagnetic–ferromagnetic phase transition of magnetic materials. In this work, the critical behavior of the lightly Ga-doped manganites Nd0.55Sr0.45Mn0.98Ga0.02O3 (NSMGO) has been investigated. Scaling analysis reveals the critical exponents β=0.308, γ=1.197, and δ=4.916, where their self-consistency and reliability are verified by the Widom scaling law and the scaling equation. These exponents indicate that the magnetic phase transition in NSMGO belongs to the anisotropic 3D-Ising universality class. Nevertheless, the asymptotic critical exponents βeff and γeff are found to approach to the values of 3D-Heisenberg model, implying the existence of isotropic short-range magnetic interactions. We suggest that, although the Nd-based manganites possess a strong magnetocrystalline anisotropy, this effect can be partly averaged out in view of the present polycrystalline NSMGO. Therefore, in the asymptotic critical region, the phase transition reveals the crossover from the scaling of 3D-Ising toward 3D-Heisenberg universality class.

Studies on the structure, critical behavior and magnetocaloric effect in (LaBi)SrCoO cobaltite

In the present paper, we report the structure, the magnetic, the critical behavior, the magnetocaloric properties and the universal curve of La0.45Bi0.15Sr0.4CoO3 cobaltite. Polycrystalline sample was synthesized in air by the solid state reaction method at a sintering temperature of 1200 °C. Phase purity, structure, size, and crystallinity were investigated using X-ray diffractometry (XRD) and scanning electron microscopy (SEM). The Reitveld refinement of XRD pattern shows that the sample adopts a rhombohedral system with \(R\overline 3 c\) space group. Critical exponents obtained by the modified Arrott plot technique, Kouvel–Fisher method, and critical isothermal analysis are close to the theoretical prediction of 3D Heisenberg model values, revealing the characteristic of short-range ferromagnetic interactions. With these values, the M(T,µ0H) relations below and above the curie temperature collapse into two universal branches in the asymptotic critical region following the scaling equation. Moreover, the experimental magnetic entropy changes measured for various fields collapse onto a master curve, confirming the universal behavior of the magnetocaloric effect in this system. Particularly, its magnetic-field dependence obeys a power-law fitting, where the exponent n = 0.98 is quite far from the value calculated at Curie temperature from the critical exponents. This difference is related to the magnetic inhomogeneity in the sample.

Isotropic-Heisenberg to isotropic-dipolar crossover and finite-size scaling in Cr75−xFe25+x (x = 0, 5) thin films

‘Zero-field’ linear ac magnetic susceptibility, χ1(T), of the Cr75−xFe25+x (x=0, 5) thin films with thickness, t, ranging from 980 to 10nm has been measured at temperatures close to Tc, the temperature at which the ferromagnetic-paramagnetic phase transition occurs. An elaborate analysis of χ1(T⩾Tc) for the films with t⩾40nm yields the temperature dependence of the effective critical exponent for susceptibility, γeff(T), that is characteristic of the three-dimensional (3D) isotropic Heisenberg-to-3D isotropic dipolar crossover. In the asymptotic critical region (ACR), these thin-film samples behave as a 3D isotropic dipolar (ID) ferromagnet. As the film thickness reduces from t≃ 980nm to 40nm, ACR narrows down while the temperature, Tdip, at which a dip in γeff(T) occurs and the temperature, TIH∗, that marks the onset of the 3D isotropic Heisenberg (IH) behavior, shift to lower temperatures. For a given t, the width of ACR as well as the characteristic temperatures Tdip and TIH∗ increase with decreasing (increasing) Fe (Cr) concentration. Consistent with these observations, the ratios involving nonlinear ac magnetic susceptibilities obey the generalized magnetic equation of state with 3D ID critical exponents and the value of Tc same as that determined from χ1(T). A quantitative comparison between theory and experiment highlights certain limitations of the existing theories. The films with t≲20nm do not exhibit 3D IH-to-3D ID crossover. Instead, the critical behavior of Cr70Fe30 thin films with t=21nm and t=11nm is that of a 3D IH and 3D Ising ferromagnet, respectively. By contrast, a 3D Ising (spin glass) critical behavior is observed in the Cr75Fe25 thin film with t=19nm (t=12nm). Curie temperature, Tc, decreases with film thickness in accordance with the finite-size scaling.

Magnetic order-disorder phase transition in Cr70Fe30 thin films

Dynamic magnetic response of Cr70Fe30 thin films with thickness in the range 11 nm ≤ t ≤ 978 nm and composition above the critical concentration for ferromagnetism was determined by measuring linear (χ1) and nonlinear (χ2 – χ5) ac-magnetic susceptibilities over three decades of frequency (101 – 104 Hz) in the temperature range 2–300 K. An elaborate analysis of χ1(T), measured in the absence or presence of a superposed dc magnetic field, Hdc, reveals that the asymptotic critical behavior of the films with t ≥ 21 nm is that of a three-dimensional (3D) isotropic dipolar ferromagnet. Interplay between long-range dipole–dipole and short-range exchange interactions causes a crossover to the 3D isotropic Heisenberg critical behavior when the temperature is increased above the Curie temperature, TC, outside the asymptotic critical region (ACR). By contrast, in the ACR, the film with t = 11 nm behaves as a 3D Ising ferromagnet. TC decreases with film thickness in accordance with the finite-size scaling with the value for the spin–spin correlation length exponent that corresponds to the 3D isotropic dipolar universality class. In the films with t ≤ 42 nm, besides the macroscopic length scale of the ferromagnetic order in the static limit, there exists a length scale that corresponds to finite spin clusters, whose dynamics is spin glass-like.

Anomalous magnetoresistance in nanocrystalline gadolinium at low temperatures

The results of a detailed investigation of electrical resistivity, ρ(T) and transverse magnetoresistance (MR) in nanocrystalline Gd samples with an average grain size d = 12 nm and 18 nm reveal the following. Besides a major contribution to the residual resistivity, ρr(0), arising from the scattering of conduction electrons from grain surfaces/interfaces/boundaries (which increases drastically as the average grain size decreases, as expected), coherent electron–magnon scattering makes a small contribution to ρr(0), which gets progressively suppressed as the applied magnetic field (H) increases in strength. At low temperatures (T ≲ 40 K) and fields (H = 0 and H = 5 kOe), ρH(T) varies as T3/2 with a change in slope at T+ ≃ 16.5 K. As the field increases beyond 5 kOe, the T3/2 variation of ρH(T) at low temperatures (T ≲ 40 K) changes over to the T2 variation and a slight change in the slope dρH/dT2 at T+(H) disappears at H ⩾ 20 kOe. The electron–electron scattering (Fermi liquid) contribution to the T2 term, if present, is completely swamped by the coherent electron–magnon scattering contribution. As a function of temperature, (negative) MR goes through a dip at a temperature Tmin ≃ T+, which increases with H as H2/3. MR at Tmin also increases in magnitude with H and attains a value as large as ∼15% (17%) for d = 12 nm (18 nm) at H = 90 kOe. This value is roughly five times greater than that reported earlier for crystalline Gd at Tmin ≃ 100 K. Unusually large MR results from an anomalous softening of magnon modes at T ≃ Tmin ≈ 20 K. In the light of our previous magnetization and specific heat results, we show that all the above observations, including the H2/3 dependence of Tmin (with Tmin(H) identified as the Bose–Einstein condensation (BEC) transition temperature, TBEC(H)), are the manifestations of the BEC of magnons at temperatures T ⩽ TBEC. Contrasted with crystalline Gd, which behaves as a three-dimensional (3D) pure uniaxial dipolar ferromagnet in the asymptotic critical region, ρH=0(T) of nanocrystalline Gd, in the critical region near the ferromagnetic-paramagnetic phase transition, is better described by the model proposed for a 3D random uniaxial dipolar ferromagnet.

Crossover effects in dilute magnetic materials by finite-time dynamics method

Crossover phenomena are ubiquitous in disordered system. However, the crossover effects from the competition between different fixed points make it hard to identify the asymptotic scaling regime controlled by the random fixed point. Therefore, the analyses on the crossover effects are of great importance to understand phase transition in dilute magnetic materials. In this paper, we derive the scaling function characterizing the crossovers to probe critical behavior. According to these, we show an alternative method to locate the asymptotic critical region in the quenched random systems in the finite-time dynamics frame. For the three-dimensional bond-diluted Ising model, the asymptotic critical exponents are identified with ν=0.686(1),β=0.356(6),α=−0.057(3),γ=1.345(20),z=2.170(11) at middle bond concentration p=0.7 from the effective ones describing the approach to the asymptotic regime for weak dilution (p=0.9) and strong dilution (p=0.5). The dynamic critical exponent from our non-equilibrium simulation supports distinctly z≈2.18 as suggested previously, as opposed to the existing larger values.

Critical behaviour of nanocrystalline gadolinium: evidence for random uniaxial dipolar universality class

We report on how nanocrystal size affects the critical behaviour of the rare-earth metal Gd near the ferromagnetic-to-paramagnetic phase transition. The asymptotic critical behaviour of the coarse-grained polycrystalline sample (with an average crystallite size of L≅100 μm) is that of a (pure) uniaxial dipolar ferromagnet, as is the case with single crystal Gd, albeit the width of the asymptotic critical region (ACR) is reduced. As the grain size approaches ∼30 nm, the ACR is so narrow that it could not be accessed in the present experiments. Inaccessibly narrow ACR for L ∼ 30 nm and continuous increase in the width of the ACR as L decreases from 16 to 9.5 nm basically reflect a crossover to the random uniaxial dipolar fixed point caused by the quenched random exchange disorder prevalent at the internal interfaces (grain boundaries).

Unravelling the nature of ferromagnetic-paramagnetic phase transition and its bearing on colossal magnetoresistance in nanocrystalline La1−xCaxMnO3 (0.3 ≤ x ≤ 0.4)

The nature of the ferromagnetic (FM)-paramagnetic (PM) phase transition at changes from first order to second order when the average crystallite size, d, falls below 100 nm in optimally hole-doped nanocrystalline La1−xCaxMnO3. In zero field, the systems with d < 100 behave as a three-dimensional (3D) uniaxial dipolar ferromagnet in the asymptotic critical region but in finite fields, the asymptotic critical behavior changes over to that of a 3D Ising ferromagnet. How effectively polaron correlations couple magnetic degrees of freedom to the lattice decides the order of the FM-PM transition and the magnitude of colossal magnetoresistance (CMR). d alters the electron-lattice coupling and thereby enables the tuning of CMR over an unusually wide temperature range.

Critical behavior in the antiperovskite Mn3CuN at ferromagnetic to paramagnetic phase transition

We have investigated the critical behavior of Mn3CuN in the ferromagnetic (FM) to paramagnetic (PM) transition. Critical behavior of Mn3CuN can be divided into two stages around Curie temperature (TC): i) ZI (T>TC) and ii) ZII (T<TC). By using various methods, including modified Arrott plot, Kouvel–Fisher (KF) method, and critical isotherm analysis, reliable critical exponents β, γ and δ are approached. With these critical exponents, magnetization–field–temperature (M–H–T) data below and above TC collapse into two universal branches in the asymptotic critical region following the scaling equation. It was found that in ZI mean-field model occupies a predominate position, while for ZII, J(r)∼r−4.8 lies between the theoretical values of 3D Heisenberg model and the mean-field model, indicating that the competition between Mn–Mn and Mn–N bonds should be responsible for the exchange interaction.

Two tests for sequential detection of a change-point in a nonlinear model

In this paper, two tests, based on weighted CUSUM of the least squares residuals, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the literature but for the linear models. It is tested under the null hypothesis, at each sequential observation, that there is no change in the model against a change presence. The asymptotic distribution of the test statistic under the null hypothesis is given and its convergence in probability to infinity is proved when a change occurs. These results will allow to build an asymptotic critical region. Next, in order to decrease the type I error probability, a bootstrapped critical value is proposed and a modified test is studied in a similar way. A generalization of the Hájek–Rényi inequality is established.Simulation results, using Monte-Carlo technique, for nonlinear models which have numerous applications, investigate the properties of the two statistic tests.

Critical behaviour of optical birefringence near the normal–incommensurate phase transition in[N(CH3)4]2ZnCl4 crystals under the influence of hydrostatic pressure

We have estimated the Ginzburg numberG governing crossover from the asymptotic to the classical criticalbehaviour near the normal–incommensurate phase transition in[N(CH3)4]2ZnCl4 (TMAZC) crystals andthe dependence of G on the hydrostatic pressure (0.1–330 MPa), following from the experimental datafor the optical birefringence and the quantitative analysis of temperaturederivatives of the birefringence in the framework of the approximation of weakGaussian fluctuations. The Ginzburg number found experimentally for TMAZC isG ∼ 8 × 10 − 3 at theatmospheric pressure and a considerable part of it is assumed to refer to structural defects. It is shownthat the G value for TMAZC decreases with increasing hydrostatic pressureand, based on analysis of the literature birefringence data forCs2CdBr4 andCs2HgBr4 crystals, this behaviour might be expected to be generally typical for all theA2BX4 family. The results obtained are discussed using a phenomenological theory of second-orderstructural phase transitions. In particular, they provide a basis for estimating thelimits of the asymptotic critical region in TMAZC and demonstrate that themajor part of the incommensurate phase should belong to the crossover region.

Multiparameter crossover equation of state: Generalized algorithm and application to carbon dioxide

In this work, we propose a new optimization algorithm for the development of multiparameter crossover equations of state (MC EOS), which incorporates the asymptotic scaling laws near the critical point. This algorithm is based on stepwise regression, which reduces the intercorrelations among the functional terms in the equation and enables the incorporation of the universal crossover formulation into the development of equations of state. The EOS developed is optimized in structure and gives correct prediction of caloric properties in the immediate vicinity of the critical point. For the determination of the linear, analytical coefficients and the non-linear crossover parameters in the crossover EOS for a given fluid, both linear and non-linear optimization procedures are used. By applying this algorithm we have developed a wide-range crossover equation of state (EOS) for carbon dioxide in the form of dimensionless Helmholtz energy. The derived MC EOS contains only 26 functional terms, and gives excellent descriptions of experimental data over a wide-range of states. Compared to the extremely accurate standard reference equation of state of Span and Wagner (SW EOS), the MC EOS yields a very good description of thermodynamic surfaces away from the critical point. In one-phase region, the MC EOS represents the experimental values of density with an average absolute deviation (AAD) of about 0.1%, and pressure with an AAD of about 0.3%. However, unlike the SW EOS, the MC EOS reproduces the well-established scaling laws behavior in the asymptotic critical region as T → T c.

Reanalysis of Microgravity Heat Capacity Measurements Near the SF6Liquid–Gas Critical Point

The earlier microgravity heat capacity measurements in SF6 by Haupt and Straub have been reanalyzed in this study. A simple power law as well as the minimal-subtraction renormalization (MSR) scheme were used to fit the measurements. In this paper the unexpected result that the SF6 heat capacity measurements appear to be within the asymptotic critical region all the way out to a reduced temperature |t| ≃ 10−2 is presented. This conclusion is in contradiction with the smaller asymptotic region |t| < 1.6× 10−4 found in the original investigation. These heat capacity measurements were found to be inconsistent with renormalization group predictions using SF6 compressibility measurements.

Rounding of a first-order magnetic phase transition inGa-dopedLa0.67Ca0.33MnO3

The effect of disorder on the critical properties of the ferromagnetic phase transition in colossal magnetoresistive manganite ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{MnO}}_{3}$ has been studied by substituting $\mathrm{Ga}$ for $\mathrm{Mn}$. It is found that, upon 10% $\mathrm{Ga}$ substitution, the peak in the specific heat at the Curie point ${T}_{C}$ changes drastically and appears as a small anomaly. Static magnetization data analyzed in the asymptotic critical region using modified Arrott plots and the Kouvel-Fisher method give values for the critical exponents $\ensuremath{\beta}=0.387(6)$, $\ensuremath{\gamma}=1.362(2)$, and $\ensuremath{\delta}=4.60(3)$. The results show that the first-order transition in ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{MnO}}_{3}$ becomes continuous by $\mathrm{Ga}$ substitution. The critical properties of the rounded transition in ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{Mn}}_{0.9}{\mathrm{Ga}}_{0.1}{\mathrm{O}}_{3}$ suggest that the magnetic subsystem in this mixed-valent perovskite is close to that of a conventional isotropic ferromagnet belonging to the Heisenberg universality class with short-range interactions. It is concluded that the first-order magnetic transition in pure ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{MnO}}_{3}$ is induced by fluctuations from a competing mode, which couples to the magnetic subsystem.

Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions.

Critical dynamics of the simple-cubic Heisenberg antiferromagnetRbMnF3:Extrapolation toq=0

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of RbMnF$_3$, treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent $z$ between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\pm 0.03$, in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at $T_c$, seen in experiments and previous simulations, but absent in the renomalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.