Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Critical behavior of Fe15Ni65B18Si2 ferromagnetic glass

AC susceptibility, magnetization and electrical resistivity around the Curie temperature (T_c) were measured for Fe₁₅Ni₆₅B₁₈Si₂ glass. The results yield T_c = (307.6±0.1) K and the following critical exponents γ = 1.50±0.03, β = 0.375±0.01, δ = 5.1±0.1 andα = -0.29±0.05. These values were obtained in the reduced temperature interval $\text{1×10}{}^{-3}\text{?}\text{|T?T}{}_{\mathrm{c}}\text{|}\text{T}{}_{\mathrm{c}}\text{?5 ×10}{}^{-2}$. In spite of the fact that these values for the critical exponents were obtained from different measurements they obey the equality relations γ = β(δ?1) and γ+2β+α = 2. Reduced magnetisation and field follow a magnetic equation of state derived for a second-order phase transition over a wide temperature range. This set of critical exponents is compared with those derived from the Heisenberg model as well as with the usual ones for a pure crystalline ferromagnets. The comparison shows that the values of |α| and γ, for our alloy, are considerably larger than those from the model and the usual crystalline ones. A similar difference is also observed in some other amorphous and dilute crystalline ferromagnets and is probably due to magnetic inhomogeneities.     

Critical properties of the three-dimensional Ising model with quenched disorder

The static critical properties of the three-dimensional Ising model with quenched disorder are studied by the Monte-Carlo (MC) method on a simple cubic lattice, in which the quenched disorder is distributed as nonmagnetic impurities by the canonical manner. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.0; 0.95; 0.9; 0.8; 0.7; 0.6. The systems of non-linear sizes L×L×L, L=20-60 are researched. On the basis of the finite-size scaling (FSS) theory, the static critical exponents of specific heat α, susceptibility γ, magnetization β, and an exponent of the correlation radius in a studied interval of concentrations p are calculated. It is shown that the three-dimensional Ising model with quenched disorder has two regimes of the critical behavior universality in a dependence on nonmagnetic impurities.     

Monte-Carlo calculation for the classical F.C.C. Heisenberg ferromagnet

The equilibrium properties of the classical f.c.c. Heisenberg ferromagnet are studied by Monte- Carlo techniques for small finite systems. Using the asymptotic dependence on the system size the results are extrapolated to the infinite system. The critical temperature is found to be T_c = 3.18 ± 0.02 and the critical exponents obtained are β = 0.33 ± 0.02, γ = 1.37 ± 0.04. The specific heat appears to have a cusp with α′_s = 0.1 ± 0.03 and α_s = 0.1 ± 0.1. Remarkable agreement is found with the finite-scaling theory.     

Effect of calcium deficiency on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.8Ca0.2MnO3 oxides

The critical behavior associated with the magnetic phase transition has been investigated by magnetization isotherms in La_0.8Ca_0.2MnO₃ and La_0.8Ca_0.1□_0.1MnO₃ (□ is the calcium deficiency). The critical exponents are estimated by various techniques such as the Modified Arrott plot, Kouvel–Fisher plot and critical isotherm technique. The critical exponents values for La_0.8Ca_0.2MnO₃ are very close to those found out by the 3D-Ising model (β=0.328, γ=1.180, and δ=4.826 at an average T_C=181.676 K). Moreover, the estimated critical exponents of La_0.8Ca_0.1□_0.1MnO₃ are consistent with the prediction of the 3D-Heisenberg model (β=0.357, γ=1.167, and δ=4.802 at an average T_C=178.182 K). We noted that the critical exponents γ are almost similar to the value of the mean-field theory which can be explained by the existence of a long-range dipole–dipole interaction. Following the Harris criterion, we deduced that the disorder in our case is relevant, which can be the cause of the change in the universality class.     

The Stückelberg holographic superconductors with Weyl corrections

In this Letter we construct the Stückelberg holographic superconductor with Weyl corrections. Under such corrections, the Weyl coupling parameter γ plays an important role in the order of phase transitions and the critical exponents of second order phase transitions. So do the model parameters cα, α and c₄. Moreover, we show that the Weyl coupling parameter γ and the model parameters cα, α, c₄ which together control the size and strength of the conductivity coherence peak and the ratio of gap frequency over critical temperature ωg/Tc.     

Crossover scaling,correlation function and connectivity in dilute low temperature ferromagnets

For quenched dilute ferromagnets with a fractionp of spins (nearest neighbor exchange energyJ) and a fraction 1 —p of randomly distributed nonmagnetic atoms, a crossover assumption similar to tricritical scaling theory relates the critical exponents of zero temperature percolation theory to the low temperature critical amplitudes and exponents near the critical lineT _c (p)>0. For example, the specific heat amplitude nearT _c (p) is found to vanish, the susceptibility amplitude is found to diverge forT _c (p →p _c ) → 0. (Typically,p _c =20%.) AtT=0 the spin-spin correlation function is argued from a droplet picture to obey scaling homogeneity but (at fixed distance) not to vary like the energy; instead it varies as const + (p _c —p)^2β +? for fixed small distances. A generalization of the correlation function to finite temperatures nearT _c (p) allows to estimate the number of effective percolation channels connecting two sites in the infinite (percolating) network forp>p _c ; this in turn gives, via a dynamical scaling argument, a good approximation for theT=0 percolation exponent 1.6 in the conductivity of random three-dimensional resistor networks. This channel approximation also givesΦ=2 for the crossover exponent; i.e. exp(?2J/kT _c (p)) is an analytic function ofp nearp=p _c . An appendix shows that cluster-cluster correlations atT=0 (excluded volume effects) are responsible for the difference between percolation exponents and the (pure) Ising exponents atT _c (p=1).     

Critical exponents of the Ising model on low-dimensional fractal media

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents β, γ, and ν are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_ef), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_ef=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.     

Total attenuation cross-sections of fluorescent X-rays of Zr,Sn, Ba,Au, Pb,Th and U in elements 6⩽Z⩽82

The total attenuation cross-sections in elements 6?Z?82 forK _α andK _β groups of lines of elements Zr, Sn and Ba andL _l ,L _α,L _β andL _γ groups of lines of the elements Au, Pb, Th and U have been measured. The experimentally measured attenuation cross-sections have been found in good agreement with the theoretical estimates.     

Critical exponents for the Reggeon quantum spin model

The Reggeon quantum spin (RQS) model on the transverse lattice in D dimensional impact parameter space has been conjectured to have the same critical behaviour as the Reggeon field theory (RFT). Thus from a high “temperature” series of ten (D = 2) and twenty (D = 1) terms for the RQS model we extrapolate to the critical temperature T = T_c by Padé approximants to obtain the exponents η=0.238±0.008, z=1.16±0.01, v=1.271±0.007 for D=2 and η=0.317±0.002, z=1.272±0.007, v=1.736±0.001, λ=0.57±0.03 for D=1. These exponents naturally interpolate between the D=0 and D=4?ε results for RFT as expected on the basis of the universality conjecture.     

Monte Carlo study of the critical behavior and magnetic properties of La2/3Ca1/3MnO3 thin films

Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La_2/3Ca_1/3MnO₃ thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La_2/3Ca_1/3MnO₃ thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn³⁺-Mn³⁺(e_g-e_g′), Mn³⁺-Mn⁴⁺(e_g-d³) and Mn³⁺-Mn⁴⁺(e_g′-d³) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56±0.01, α=0.16±0.03, β=0.34±0.04γ and γ=1.17±0.05. These theoretical results are consistent with the Rushbrooke equalitiy α+2β+γ=2.     

Precise atomic masses of147Eu,147Gd,and151Tb derived from their decay properties

Theβ-decay energies of¹⁴⁷Eu,¹⁴⁷Gd, and¹⁵¹Tb were determined by usingγ-spectroscopical methods. The comparison of experimental with calculatedK-capture probabilities yielded theQ _EC values 1.690( _?16 ⁺²¹ )MeV and 2.203( _?13 ⁺¹⁹ )MeV for¹⁴⁷Eu and¹⁴⁷Gd, respectively. By measuring the ratio of positron decay to electron capture for two branches in¹⁴⁷Eu decay, the decay energiesQ _EC=1.702(13) MeV andQ _EC=1.709(18)MeV were derived. Also fromEC/β ⁺ ratios the valuesQ _EC=2.225(75) MeV for¹⁴⁷Gd, andQ _EC=2.566(12)MeV for¹⁵¹Tb were obtained. Earlier discrepancies in the mass adjustment of these isotopes were removed. In course of the present studiesγ-decay properties of¹⁴⁷Eu and¹⁴⁷Gd were reinvestigated.     

Analysis of the evaporation-corrected mass and charge distributions in the Ar+Mo reactions

Partly and strongly damped fragments from the reactions³⁶Ar+⁹²Mo and⁴⁰Ar+¹⁰⁰Mo are measured atE _Lab=270 MeV. The extracted mass and charge distributions are carefully corrected forγ, n, p andα particle evaporation. The resulting primary distributions are analysed with theoretical models which assume statistical neutron and proton exchange on the potential energy surface of the projectile-target system. Dynamical-deformation effects in the framework of the surface friction model are included.     

引入“鬼”场的二维次近邻正方格点渗流模型的重整化群方法研究

应用位置空间重整化群方法,对引入“鬼”场的二维次近邻正方格点渗流模型进行研究,得到临界值P_c和临界指数α,β,γ,ν,δ,η。     

Spin glass behavior and critical analysis across the magnetic phase transition in Gd2CoMnO6: dc magnetization and ac susceptibility study

We report here on critical analysis across magnetic phase transition and spin dynamics in Gd₂CoMnO₆. We found that this material behaves differently below and above the applied magnetic field of 20 kOe. The magnetic phase transition switches from nearly mean-field type to unusual class and T_c shifts towards the high temperature above 20 kOe field. The nature of the magnetic phase transition is explored by carrying out critical analysis at low as well as at high magnetic field. The critical exponents obtained at low field using Kouvel-Fisher method are β = 0.65 (2) γ = 0.90 (2), δ = 2.43 and T_c = 120 K. Apparently, these values of critical exponents appear close to mean-field model. For high field the critical exponents are β = 1.24 (2) γ = 0.64 (5), δ = 1.51 (3) and T_c = 128 K. The critical exponents show significant deviation from any universal class. This switchover in the nature of the magnetic phase transition is unique and not seen in many compounds. The formation of non-Griffiths-like clusters in this compound can be a reason for such unique behavior. Further, ac susceptibility has been measured to understand the spin dynamics in detail. The dispersion of frequency-dependent χ_ac below T_c confirms a spin glass state in this material. The observed value of τ_o and T_o indicate the slow dynamic spin which is caused by co-existence of Co/Mn spin magnetic moments. The magneto-caloric effect is also presented for Gd₂CoMnO₆ in this study. The magnetic study and critical analysis across the phase transition reveal a switchover in the nature of phase transition in this material. A non-Griffiths like cluster formation above T_c is found and dynamic susceptibility study reveals a spin glass state below T_c in Gd₂CoMnO₆.     

Spectral shifts and spectral switches of spatially and spectrally partially coherent pulsed beams in Young’s interference experiment

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio ε, temporal coherent length T_c, spatial correlation parameter β and diffraction angle α. It is shown that the critical angle α_c of the first- and second-order spectral switches moves away from the z axis with increasing T_c, but α_c of the third-order spectral switch moves towards the z axis with increasing T_c. The spectral transition height Δ decreases and spectral minimum S_min increases as T_c increases. α_c decreases, Δ increases and S_min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.     

Majority-vote on directed Erd?s-Rényi random graphs

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter q_c, as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.     

Correction to scaling critical exponents and amplitudes for amorphous Fe–Mn–Zr alloys

Asymptotic and leading correction to scaling critical exponents and amplitudes have been determined for quenched amorphous Fe_90−yMn_yZr₁₀ (y=0–8) ferromagnets through an elaborate analysis of temperature dependence of spontaneous magnetization, zero-field susceptibility and low-field AC susceptibility data obtained in the asymptotic critical region. From this analysis, it is found that the values of the critical exponents and amplitudes do not depend on the alloy composition and are in good agreement with the values predicted for three-dimensional Heisenberg ferromagnet system. The observed experimental results are consistent with the concept of scaling in that the exponent equalities β=γ(δ−1) and α=2(1−β)−γ are obeyed to a high degree of accuracy. These results show that both amorphous and crystalline materials behave similarly in the critical region though amorphous alloys show a wide asymptotic critical region than the crystalline materials. The presence of disorder does not seem to have any influence on critical behavior of the system investigated in the present work.     

High-resolution X-ray emission Lα1 and Lβ2 Spectra of Hf, Ta, W, Re, and Os

The shape and relative intensities S _α=I(α_1s )/I(α_1s ), S _β=I(β_1s )/I(β₂) of the short-wavelength X-ray Lα₁ and Lβ₂ satellites arising from the radiative decay of the states corresponding to L ₃ M _4,5 configurations were investigated experimentally for Hf, Ta, W, Re, and Os. It was established that, in the case of W, the values S _α=2.5%, S _β=4.2% are five to seven times larger than those for Hf and Ta, and by (30–60)% smaller than those for Re and Os. On the basis of the obtained values of S _α,S _β, as well as the observed two-component structure of the Lα₁ and Lβ₂ satellites, it is concluded that the Coster-Kronig L ₁-L ₃ M ₅ transitions (CK) are allowed by the energy conservation law even for tungsten, and, starting with this element, they represent a major channel of generation of the states of LL ₃ M ₅ configuration. Possible features of such a process for the W atom are discussed in comparison with those for Re and Os.