Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.     

A generalized cluster theory of disordered alloys extended to include random off-diagonal elements

The generalized cluster expansion of the coherent potential approximation as applied to the case of a disordered binary alloy is discussed and extended to include the case of random off-diagonal elements of the Hamiltonian. Numerical results are presented.     

Self-consistent perturbation theory for the vibrational spectra of certain disordered systems

The effect of coupling parameter fluctuations (quantitative disorder) on the vibrational spectrum of a solid is investigated. Since small deviations from crystalline order already turn out to lead to considerable broadening of the crystalline spectrum, a self-consistent perturbation scheme is developed similar to the coherent potential approximation for electronic systems. An approximate equation is obtained in which disorder is described in terms of a single dimensionless parameter which is a measure of the mean square fractional deviations of the coupling parameters from their average values. The equation is solved self-consistently by iteration. The final result is a convolution expression for the amorphous spectrum in which all van Hove singularities are smeared out except the ones at zero frequency and at the upper cutoff of the spectrum. Numerical results are obtained for silicon using a Keating crystalline density of states and assuming that the average values of the coupling parameters are identical to the crystalline ones. The maxima of the crystalline spectrum are broadened but qualitatively retained to a larger extent than in a simple convolution of the spectrum with a Gaussian.     

Effective field theory for disordered magnetic alloys

Disordered alloys of magnetic atoms of two types have been considered within the Ising model based on the calculation and analysis of the distribution function of effective fields acting on magnetic atoms. The Curie temperatures, magnetizations of two magnetic “sublattices,” threshold concentrations of magnetic atoms, and magnetic phase diagrams of alloys have been calculated.     

Magnetism in FeNiW disordered alloys: Experiment and theory

We report here an experimental study of magnetization of FeNiW alloys at different compositions. We have studied variation of magnetization with temperature (at low external fields) and magnetic field (at low temperatures). The alloy shows para to ferromagnetic transitions across the composition range. We do not find any indication of the spin-glass phase. We have supplemented the experimental work with theoretical analysis using the first-principles tight-binding linear muffin-tin orbitals based augmented space recursion method. Our theoretical estimates of magnetic moment and Curie temperatures agree well with experiment. Our mean-field phase analysis also does not indicate the possibility of a spin-glass phase.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

Self-consistent theory of Bose-condensed systems

In the theory of Bose-condensed systems, there exists the well known problem, the Hohenberg–Martin dilemma of conserving versus gapless approximations. This dilemma is analysed and it is shown that it arises because of the internal inconsistency of the standard grand ensemble, as applied to Bose systems with broken global gauge symmetry. A solution of the problem is proposed, based on the notion of representative statistical ensembles, taking into account all constraints imposed on the system. A general approach for constructing representative ensembles is formulated. Applying a representative ensemble to Bose-condensed systems results in a completely self-consistent theory, both conserving and gapless in any approximation.     

Self-consistent Hückel theory

Systematic approximations to the Pople method lead to a form of Hückel theory which is self-consistent with respect to charges and bond orders. The method is applied to the calculation of ionization potentials, electron affinities and equilibrium bond lengths in conjugated molecules.     

Landau levels in disordered alloys

The electronic structure of a substitutionally disordered alloy in a uniform magnetic field has been studied on a simple model of scattering potentials (zero range potentials). The coherent potential and single-site aproximation have been employed. It turned out that in wide energy region the Dingle temperature, characterizing the decay of the amplitude of de Haas — van Alphen oscillations, is determined by the part of self-energy which does not depend on magnetic field. The field dependent part is important only for a few Landau levels at the bottom of the band. The results can be applied to simple metals and semi-metals.     

Self-consistent scaling theory for logarithmic-correction exponents

Multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature, and some new predictions for logarithmic corrections in certain models are made.     

Electronic structure of disordered BCC alloys

This paper describes and analyses a self-consistent cluster coherent potential approximation calculation of the electron density of states of a random, binary alloy on abcc lattice.