Table of contents

The critical properties of the three-state Potts antiferromagnet on a square lattice have been investigated by 'large-cell' renormalisation using an exact numerical technique. The results indicate the existence of a single fixed point at beta ^-1=0.

Brownian trajectories, obtained from molecular dynamics simulations of two-dimensional systems with inverse power-law potentials, exhibit fractal behaviour. The fractal dimensionality D goes to two asymptotically. The approach to the asymptotic value depends on the thermodynamic state of the system. Experiments are proposed to verify the authors' predictions for the behaviour of D.

The equilibrium configuration of the self-trapped exciton (STE) in CaF₂ and SrF₂ is calculated by minimising the total energy of the crystal containing an excited electron and a self-trapped hole. The electron is treated by the ion-size method and the lattice by pair potentials. It shows very clearly that the STE in fluorites is not equivalent to a V_k centre plus an electron, but is closer to a F+H pair. It is also shown that only one of the four possible configurations is directly realised after the self-trapped hole captures an electron. The interconversion between the different configurations is briefly discussed.

The photoluminescence at 10K in HB- and LEC-grown GaAs:V has been studied in the spectral range 0.7-1.52 eV. In n-type HB-grown samples the increase of V concentration hinders the formation of donor-Ga-vacancy complexes. In V-compensated semi-insulating LEC samples, in addition to the well known PL band, which is due to V_Ga³⁺(3d²) centre, a broad band at 0.8 eV has been found to be V-related. It probably indicates the presence of a second acceptor-type centre, which should be responsible for the compensation in V-doped gallium arsenide.

The conductivity sigma for electron transport via strongly localised electron states in a one-dimensional MOSFET has been determined by the direct solution of the Miller-Abrahams equivalent network equations (1960). Random fluctuations of log sigma proportional to T^-1/2 are observed as the chemical potential mu moves through an energy band of width W. The fluctuations are smaller than those determined recently by Lee (1984) using a percolation argument and the proportionality constant is 60% higher. As the temperature decreases the fluctuations increase from approximately one order of magnitude when kT/W=0.008 to approximately nine orders of magnitude when kT/W=0.001. The conductivity decreases to an asymptotic limit as the length of the system increases.

The scaling laws derived by Grinstein (1976) for the random-field Ising model (RFIM) are rederived on the assumption that the transition is second order and that the critical behaviour is controlled by a zero-temperature fixed point. The scaling laws involve three independent exponents nu , eta and gamma , the last appearing in a modified hyperscaling relation, 2- alpha =(d-y) nu . It is argued that such hyperscaling modifications are a general feature of phase transitions controlled by zero-temperature fixed points. Explicit evaluation of the RFIM exponents in d=2+ epsilon dimensions, yields, to order epsilon , 1/ nu = epsilon , eta =1- epsilon /2 and y=1+ epsilon /2. The exponent nu is different from that of the pure model in (d-y) dimensions implying that no exact 'dimensional reduction' is possible near two dimensions.

The authors derive a theory of the chemical shift ( sigma ) in solids and show that sigma contains, in addition to the usual diamagnetic and paramagnetic shielding terms, a more important new term due to the spin-orbit interaction. The theory presented in this Letter is, they believe, the most general and thorough treatment which has yet been made of this problem.

The ensemble averaged amplitude correlations of a disordered harmonic system with force constant disorder are evaluated in the low-frequency (acoustic mode) range with the aid of a perturbation scheme valid for any degree of disorder. Explicit results are obtained for the amplitude correlations of linear chains in terms of the dispersion law and attenuation of acoustic waves, and compared with the case of mass disorder. Force constant disorder has a slowing down effect on the acoustic waves, which is absent from random mass disorder up to second order in the frequency. The amplitude correlation function of mass disordered systems is a single damped cosine wave while in the case of force constant disorder it consists of a group of interfering damped cosine waves associated with the group of sites coupled to a central site by a non-zero force constant element.

A self-consistent cluster effective-medium approximation for hopping transport on lattices with random traps is constructed by taking into account hops between nearest neighbours only. The quasi-particle kinetic characteristics as well as the occupation distribution function for the ensemble of sites with fixed energy levels are studied. The results obtained are shown to be exact in nearly all limiting cases, except for irreversible trapping and trapping by sinks.

The theory of quantum liquids based on applying the variational principle to a Jastrow-type trial function is combined with a Hartree-Fock-type approach. It leads to a great simplification e.g. in comparison with the theory of electrons in a solid, where the trial function is assumed to be in the form of a Slater determinant. It is shown how one can benefit from this feature in computing the screening cloud distribution around positive particles embedded in an electron gas. The numerical results have been found for a light impurity (a positron) as well as for a heavy one (a proton) over a wide range of r_s. The positron annihilation rates lambda have been calculated for the metallic densities and in the limit of large r_s. The proper behaviour of lambda has been observed especially at low densities.

An ab initio Hartree-Fock (HF) pseudopotential approach to the ground-state properties of silicon is presented. The methods used is the plane-wave self-consistent band calculation in the HF approximation. Results for the equilibrium lattice constant, cohesive energy, bulk modulus, charge density and band structure are given. The correlation contribution neglected in the HF approximation is discussed.

The band-gap fluctuation model of amorphous semiconductors is derived from a generalisation of the electron-phonon interaction. This approach shows that the lattice of an amorphous material can be described in terms of topological disorder that does not interact with the band-edge states, and random deviations from the ideal disordered lattice that act as frozen phonons. The exponential Urbach tail in both crystals and amorphous materials is derived from the calculation.

The authors present a real-space inversion of the dielectric response function of an insulator in a closed form. This is applied to the problem of a planar surface. It is shown that for a point external charge the classical 'image' results follow directly from the long-range behaviour of the inversion matrix.

Photo-ionisation cross-section spectra for holes have been studied in iron-doped GaAs_1-xP_x and optical threshold energies for the transitions from the iron levels into the valence band have been determined for a large range of compositions. The relative position of the states and the crystal-field-splitting energies were found to increase with increasing x. The ratio of the optical transition probabilities from the ground and excited state into the valence band changes for varying compositions almost symmetrically about the mid-point x=0.5. By studying thermal emission and capture rates, nonexponential dark-capacitance transients were obtained. Apparent thermal activation energies showed a dependence on x different from that of the optical data. The variation of the iron levels with x can be understood within the framework of the vacuum level reference hypothesis.

A system of dilute impurity concentration with short-ranged potentials in the presence of a very strong magnetic field is investigated. Realistic potential models such as the Thomas-Fermi potential are considered. The potential models are approximated in a systematic fashion to obtain the t-matrix in a closed form. Such potential models are nonlocal and their nonlocality alters the velocity operator which in turn changes the transport properties of the system. This aspect of the theory is very important and is correctly taken care of in this work. A generalisation of the Nozieres result is obtained for the Hall conductivity sigma _xy plus a correction term which is very important in the case of strong potential scattering.

The authors study the critical properties of the 3D quantum Heisenberg ferromagnet with random anisotropies; that is, the coupling between any pair of nearest-neighbouring spins can be either isotropic (Heisenberg) or anisotropic (Ising-or XY-like) at random. Within a Migdal-Kadanoff approximation they obtain the full critical frontier and correlation length critical exponents. They found that the isotropic Heisenberg model is unstable (in the context of universality classes) in the presence of a small concentration of couplings with lower symmetry.

The thermodynamic Bethe ansatz equations of the n-channel Kondo problem have been solved numerically. Complete compensation of the impurity magnetic moment and Fermi liquid behaviour at low temperatures is obtained if the impurity spin S is equal to n/2. At high temperatures a qualitatively new behaviour is found for large n. For n>2S the crossover to the scaling regime described by critical exponents has been calculated numerically.

The platinum(III) state in single crystals of Pt(en)₂X(ClO₄)₂ (X=Cl, Br and I) has been detected by EPR. The values of g/sub /// and g_{perpendicular to} have been determined to be 1.956 and 2.299 respectively for X=Cl, 1.980 and 2.276 respectively for X=Br, and 1.962 and 2.253 respectively for X=I at 295K. Hyperfine splitting was observed below 150K in X=Cl. Its intensity ratio with the magnetic field perpendicular to the b axis shows that the two adjacent platinum ions with total nuclear spin I=0, ¹/₂ and 1 contribute to the hyperfine structure with the following values assigned to A:A/sub ///=610 and A_{perpendicular to} =379, in units of 10^-4 cm^-1 at 77K. As for X=Br and I, the signal remains unsplit being a broad line with width 200 G down to 4.2K. Above 100K, line narrowing was observed with activation energies 5.9 and 8.5 meV respectively. The spin concentrations were determined to be of the order of 10²⁰ mol^-1 for all salts at 295K. The electrical conduction mechanism in these chain complexes are suggested to be based on EPR and optical absorption data.

The photoelectron spectroscopic binding energies of Se 3d_5/2, O 1s, and Cl 2p_3/2 or Re 4f_7/2 have been measured in tetralmethyltetraselenafulvalenium (TMTSF) perchlorate and perrhenate, tetrabutylammonium perchlorate and perrhenate, and potassium perchlorate and perrhenate. It has been found that the binding energies of Se 3d_5/2 are the same in the perchlorate and the perrhenate even though the spectrum is more asymmetrically broadened in the perrhenate. The binding energy of O 1s depends on the cation and on the central atom in the anion. In the organic perrhenates it is at 530.96 eV, whereas in the perchlorates it is at 532.08 eV. In the potassium salts the O 1s binding energies differ by 1.89 eV in the perchlorate and the perrhenate. The binding energies of Cl 2p_3/2 and Re 4f_7/2 differ by 0.84 and zero respectively from those in the potassium salts. The energetic differences among the values for O 1s indicate the extent to which the electronic structure of the TMTSF salts are determined by the electronic structure of the anions. The difference in binding energies between the TMTSF perchlorate and perrhenate is such that the application of pressure to the perrhenate should transfer electrons to the cation and presumably to the conduction band.