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     

On the berger approximation: A critical re-examination

Since the first paper by Berger some two decades ago, the simplification known as the Berger approximation has been invoked by the authors of several score papers in spite of the fact that no rational mechanical basis for the approximation could be found. Many recent papers have raised doubts on its applicability. In this paper, using certain well known results from the two dimensional theory of elasticity, a plausible explanation for the origin of the Berger method is suggested. The arguments can be developed further to show that other specious Berger-like approximations can be developed, all of them leading to uncoupled non-linear equations yielding different overall results. Further, it is shown that such methods fail to predict the non-linear behaviour with respect to important parameters and that whatever accuracy is obtained in the solution of a particular problem can at best be attributed to fortuity.     

Parton distributions in the small-x region within LLX approximation

The solutions of Lipatov-Fadin-Kuraev equation (LFK) within LLX approximation for gluon distributions are studied. The results are based on the semiphenomenological boundary conditions taken from LLQ² analysis. We find, that pure theoretical LLX approach can reproduce the form of singular small-x behaviour of gluon and sea-quark distributions obtained within LLQ²A with singular input parametrizations. Some remarks about shadowing corrections are presented.     

The static generalized susceptibility for a ferromagnet in the critical region

A method of calculating the static generalized susceptibility for the critical region in the constant coupling approximation has been formulated and applied to ferromagnets above the Curie point, leading to an anisotropic susceptibility.     

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.     

Test of the Q-space approximation in nuclear response theory

The electric monopole states are solved in TDA with a separable interaction taking into account the continuum. These results are compared with the Q-space approximation, in which the configuration space is discretized by using the harmonic oscillator basis, and the continuum is taken into account via the escape width. The Q-space approximation is found to be very good.     

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.     

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.     

Test of the validity of the adiabatic approximation in scattering theory

Exact solutions for the scattering of a fast projectile x on deuterium are compared with various versions of the fixed scatterers approximation. The content of the approximations for a nucleon and a different projectile is discussed. The calculations show the approximate agreement of angular distributions in forward direction and the amount of disagreement in the backward hemisphere. In the case of nucleon scattering the importance of nucleon exchange, neglected in the FSA, is explicitly demonstrated. As expected, the quality of the tested approximations rapidly improves with diminishing mass ratio M_x/M_N.     

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.     

PVT properties of sulfur-hexafluoride in the gas-liquid critical region

The PVT properties of sulfur hexafluoride in the critical region have been measured by using a combination of the Burnett and the isochoric methods. The measurement of one reference PV-isotherm at about 333 K was performed by the Burnett method of repeated expansions; the measurement of a large number of PT quasi-isochores between 313 and 333 K relied on the so-called isochoric method. An important feature of the data analysis is the application of several consistency criteria to the least-squares analysis for polynomial representation which made it possible to determine reliable values of the Burnett constants and the virial coefficients. The reference isotherm with 105 data points covers a pressure range between 1 and 100 bar and a density range up to 1.2 g cm^?3. The 21 isochoric runs with densities between 0.1 and 1.2 g cm^?3 contain 220 data points. Except for the region very close to the critical point, the accuracy of the measurements is estimated to be better than 0.01% in the pressure, 0.02% in the density and 1 mK in the temperature.     

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.     

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.     

The double logarithmic approximation of deep inelastic leptoproduction in the quasielastic region

We determine the asymptotic behavior of the deep inelastic leptoproduction structure functions in the quasielastic region z → 1 in the leading double logarithmic approximation of QCD. It is shown how the asymptotic behavior is related to the ON/OFF limit of the Sudakov form factor. The running coupling constant is incorporated by comparing the double logarithmic approximation with the solution of the renormalization group equation. We compare our result with various suggestions to improve the convergence of the perturbative expansion in the quasielastic region.