Nonuniversal properties in the dipolar critical region of uniaxial ferromagnets

The amplitude of the critical isotherm is expressed by microscopic magnetic parameters and the transition temperature. The agreement between calculated and experimental values is good for GdCl₃ and LiTbF₄, whereas for DyEs a discrepancy is observed.     

Nonlinear excitations in the critical region

The free energy transformation due to fluctuations is investigated in an exactly solvable model. This model accounts for the fluctuation interaction in a reduced manner and leads to a realistic estimation for the free energy. In particular it gives a nice critical exponent=5. It is shown that in spite of the monotonic character of the effective free energy in the critical region the properties of the system should be described on the basis of the ⁶ model. Localized nonlinear excitations are found to be possible with a profile rather like that known as a bump near the point of the first-order phase transition.     

Sweeping through the critical region

We present a detailed theoretical analysis of passing the critical region of a second order phase transition with finite speed of change of the control parameter. This analysis is performed both for weak and strong external fields and for an arbitrary dimension of the medium.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Thermodynamic critical amplitudes in the dipolar critical region of a uniaxial ferromagnet

In zero magnetic field susceptibility, magnetization and specific heat of GdCl₃ follow below t = |T/T_c - 1| ≈0.015 mean field laws with logarithmic corrections. Their amplitudes characterizing the strengths of the singularities are related by an equation predicted by the theory of Larkin and Khmel'nitzkii.     

Solutions of the Percus-Yevick and hyper-netted chain equations near the gas-liquid critical point

An intuitive approach is used to develop a theory of the transverse current correlation function in simple liquids. The memory function obtained on the basis of this approach is expressed in terms of the velocity autocorrelation function for the kinetic part and in terms of the radial distribution function, the interatomic potential and a time-dependent term which describes the relative motion of two atoms in the liquid for the potential part. The results for the memory function and the frequency spectrum are found to be in satisfactory agreement with the computer simulation studies of Levesque et al.     

On the solutions of the hypernetted chain equation inside the gas-liquid coexistence region

We present a detailed study of the solutions of the hypernetted chain integral equation inside the gas-liquid coexistence region for simple Lennard-Jones fluids. The study is performed by means of a hybrid Newton-Raphson algorithm extended to cope with complex solutions. In this way, we have unequivocally confirmed that the origin of the well-known HNC singular behavior inside the coexistence curve is linked to the onset of complex solutions. As density is increased starting from the vapor phase along isotherms inside the coexistence region, another singularity is encountered (very likely linked with the existence of a complex multiple solution point), and correlations start to diverge. Therefore, with the numerical approach here presented it is not feasible to join the liquid and vapor phases through an analytically continuous path of real and complex solutions. Finally, a study of the transition from the mean spherical approximation behavior (characterized by the presence of a spinodal divergence) to the peculiar hypernetted chain sort of singularity is also presented.     

The two-dimensional coulomb gas in the critical region

We consider the two-dimensional Coulomb gas in the critical region. To avoid the well-known collapse of the system below a certain temperature, the Coulomb interaction is cut inside a core radius. By analysis of the pair correlation function we find that this system exhibits a phase transition with a critical point. Below the critical temperature the ions are unable to shield each other, and they all may be considered as bound in neutral dipolar pairs. The density of dipolar pairs affects the critical temperature. In the critical region we obtain explicit results, and we are able to extract the leading singular behavior of the pair correlation function.     

Test for the cumulant approximation in the critical region

A cumulant approximation in wide use is tested, in the critical region, against a straightforward product-average decomposition approximation previously used in conjunction with a new integral representation for the Ising model. It is found that for the calculation of the transition temperature, the cumulant approximation is significantly inferior to the product-average approximation.     

Ultrasonic propagation in multicomponent system in the critical region

Ultrasonic propagation in a system consisting of coconut oil and carbon tetrachloride has been considered as a function of temperature nearTc in the low MHz region. A small velocity dispersion is seen in the system. The experimental results have been analysed with recent theories developed by Ferrell and Bhattacharjee. The data on attenuation per wavelength nearTc agree with the scaling relation developed by Kroll and Ruhland.     

Magneto-optic study of the critical region of EuS

Critical exponents of the insulating ferromagnet europium sulfide are determined using the technique of Faraday rotation. Values obtained are γ = 1.06 ± 0.05, β = 0.335 ± 0.01, δ = 4.20 ± 0.1 and T_c = 16.52 ± 0.02 K. The data are found consistent with the scaling hypothesis.     

Observation of critical slowing down of ortho-positron quenching rate near gas-liquid transition

Thermalized ortho-positronium life time spectra have been measured in xenon gas along three different isochores. The quenching rate as a function of T-T₀ shows a striking similarity to the critical slowing down of density fluctuations as measured by the Rayleigh scattering of light.     

Neutron depolarization by amorphous magnets in the critical region

The depolarization of neutrons by transmission through amorphous samples of NdFe₂ and HoFe₂ has been measured at temperatures in the neighborhood of their magnetic transitions. The results, when compared to other determinations of the Curie temperature (T_c) suggest that T_c may not be a well-defined quantity in these materials.     

Generalized perturbation theory of classical fluids in the critical region

Perturbation theories of classical fluids are extended in the critical region by decomposition of the attractive part of the pair interaction. The generalized theory is in agreement with scaling, has the correct dependence on dimensionality and on the range of the forces and offers a method to compute critical indices.     

Theoretical methods in the critical region of a phase transition

In this review we survey the various experiments completed or in preparation, which are designed to probe the anomalous magnetic moment of the muon to greater and greater precision. The emphasis lies particularly on the general issues involved and also on the most recent developments.     

Neutron refractive index of liquid mixtures in the critical region

Size effects in neutron optics of mesoscale liquid mixtures in the critical region are studied. It is shown that the Schrödinger equation for the neutron wave function can be presented as the corresponding electrodynamical wave equation with the Fermi pseudopotential for a binary liquid mixture taken into account. Formulae for the neutron refractive index of bulk and confined liquid mixtures are derived and discussed. As an example, numerical calculations for a mixture of ethane and carbon dioxide C₂H₆-CO₂ are presented, which illustrates a good agreement between experimental and theoretical data.     

Structural and vibrational properties of PVT grown Bi2Te3 microcrystals

High-quality Bi₂Te₃ microcrystals have been grown by physical vapor transport (PVT) method without using a foreign transport agent. The microcrystals grown under optimal temperature gradient are well facetted and they have dimensions up to ～100 μm. The phase composition of grown crystals has been identified by X-ray single crystal structure analysis in space group R3?m, a=4.3896(2) Å, b=30.5019(10) Å, Z=3 (R=0.0271). Raman microspectrometry has been used to describe the vibration parameters of Bi₂Te₃ microcrystals. The FWHM parameters obtained for representative Raman lines at 61 cm^?1 and 101 cm^?1 are as low as 3.5 cm^?1 and 4.5 cm^?1, respectively.     

Size of the critical region in long-range Ising spin glasses

The size of the critical region for long- but not infinite-range Ising spin glasses is calculated by looking at the single loop corrections to the Bethe lattice approximation. The size of the critical region is predicted to go as $\text{1}\text{Z}$ for large Z, where Z is the number of interacting neighbors.