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Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at $T=\infty$ are investigated numerically from the point of view of a phase transition. Branching annihilating random walk of the ferromagnetic domain boundaries determines the steady state of the system for a range of parameters of the model. Critical exponents obtained by simulation are found to agree, within error, with those in Grassberger's cellular automata., 10 pages, Latex, figures upon request, SZFKI 05/94

The inelastic mean free path of electrons (IMFP) is an important material parameter for description of electron transport processes in solids. This parameter is particularly useful for quantifying the electron spectroscopies, in particular Auger electron spectroscopy, X-ray photoelectron spectroscopy, electron energy loss spectroscopy and elastic peak electron spectroscopy. In this work, a brief overview of the IMFP determination is presented. Generally, there are two groups of methods to determine the IMFP: (i) calculations using the theoretical model based on the experimental optical data, and (ii) calculations using theory relating the IMFP and the measured probability elastic electron backscattering from solids. Major advances in the development of the second group of methods were made in three laboratories; these advances are reviewed here. The elastic backscattering probability, in absolute or relative units, can be conveniently evaluated from the elastic peak intensity. However, much effort is needed to develop the theory for calculating the IMFP, which typically involves the Monte Carlo simulations of electron trajectories in solids. Presently, this theory and typical procedures of the spectra processing are implemented in the software package EPESWIN developed by Jablonski. In recent years, much attention is devoted to the phenomenon of the electron energy losses in the surface region of solids. Reliability of the theory of elastic backscattering is distinctly improved if this effect is taken into account.

It is shown that in the framework of a generalised Ginzburg-Landau scheme based on the microscopic model of chains of 1D Fermi gases interacting via a Coulomb-type interaction it is possible to account for the observed critical behaviour near the 53K phase transition of TTF-TCNQ. The pseudogap is also calculated and its effect on the electronic density of states is found to disappear above the critical region.

In strongly anisotropic quasi-1D metallic systems the charge density wave (CDW) phase transition is given a generalised Ginzburg-Landau theory on the microscopic basis of the Gorkov-Dzyaloshinskii model. In the derivation of the free energy the interchain interaction is treated in MF approximation while the interchain interactions appear through the divergent (at T=0) CDW susceptibility chi 1DCDW of the 1D system. The exponent of chi 1DCDW is found to be the only decisive factor in determining the width of the Ginzburg critical region for a fixed interchain force range. The specific heat is also calculated and discussed.

A one-dimensional model of a metal is generalized by assigning a component index to the electron creation and annihilation operators. In the limit in which the number of components n goes to infinity it is found that a mean-field-type phase transition occurs at a finite temperature even for short-ranged interactions. It is shown that this result is not in contradiction with general theorems concerning ODLRO.

A general dynamical scaling theory of phase transitions is established by exploiting the absence of a characteristic length in an extended system at its phase transition. This similarity property imposes strong constraints on the frequency and wave-number dependence of the fluctuation spectrum and leads to unambiguous predictions concerning the critical properties. The theory is worked out in detail for the lambda transition of liquid Helium, as a prototype. The fluctuations resulting from density waves at low temperature and from both first and second sound at higher temperatures, are closely examined. The connection between the divergent fluctuations in the second sound modes (as the temperature T approaches the lambda temperature Tλ) and the critical variation of the damping coefficients is established. The critical temperature dependences of the thermal conductivity of He I and the damping of first and second sound in He II are predicted to be essentially (T − T λ ) −1 3 , (Tλ − T)−1, and (T λ − T) −1 3 . (There occur also logarithmic factors.) Recent experimental measurements of the first and second of these give quantitative verification of the theory. In addition to the temperature dependence, the dynamical scaling theory does not employ any adjustable parameter and consequently also predicts the absolute magnitude of these quatities. Although this is a less conclusive check on the theory, the agreement is also satisfactory.

A one-dimensional system of electrons interacting via a BCS-type interaction is investigated by renormalization group techniques in two successive approximations atT=0, keeping only a single energy variable ω. The first approximation is equivalent to the summation of leading logarithmic terms carried out by Bychkovet al., and correspondingly the vertex function displays a singularity at a finite value of ω. The second approximation accounts for the next leading logarithmic terms as well, and by this means the singularity is shown to be pushed down to ω=0. Due to important self-energy contributions, however, the invariant couplings behave differently and tend to a saturation value at ω=0.

The critical change in the entropy is calculated. As experimental tests, the theory predicts anomalous dispersion of second sound in bulk HeII and a logarithmic dependence of the specific heat of a HeII film upon its thickness.