Table of contents

The mean-field theory of the three-dimensional, three-state chiral Potts or asymmetric clock model is analysed and the phase diagram is determined. The model which is simpler than the ANNNI model exhibits commensurate and incommensurate spatially modulated ordered phases.

The author studies bond percolation on three-dimensional lattices. The SC lattice is considered as self-dual, while the FCC and diamond lattices are a dual pair. He conjectures a duality transformation and obtains the critical percolation probability p_c to be ¹/₄ for the SC lattice. For the diamond and FCC lattices, he uses a tetrahedral-pyramid transformation and obtain p_c to be 0.3882 and 0.1118 respectively.

The model of staging recently proposed by Millman and Kirczenow (1982) (MK) is used to examine the phase diagrams predicted for alkali metal graphite intercalation compounds. For both attractive and repulsive in-plane interactions the finite-temperature calculations based on this model yield the staged structures which are observed experimentally. The differences between the predictions of the MK model and those of other models, possible improvements to the MK model, and the implications for experiment are also discussed.

An analytic solution for the n vector textures in superfluid ³He-B in a rotating cylinder is obtained at high magnetic fields. The azimuthal angle alpha of n is found to change from 60 degrees at the wall to 38 degrees in the bulk liquid. The calculated spin wave spectrum in the stationary case is in good agreement with the Helsinki NMR experiments. In the rotating case a comparison with experiments allows the authors to estimate the orientating effect of vortex cores on the n texture. The vortex radius is expected to be of the order of 10 xi in order for the observed effects of rotation on the NMR spectrum to be explicable.

Preliminary results of the temperature and magnetic field dependence of the conductivity of narrow silicon accumulation layers are presented. Channels approximately 1 mu m wide at temperatures T approximately 1K exhibit positive magnetoconductance and Shubnikov-de Haas oscillations characteristic of weakly localised two-dimensional systems. As T is reduced, conductivity drops rapidly into a power-law behaviour, and low-field magnetoconductance changes sign. This the authors argue is the result of a transition to one-dimensional conduction, and they show that the transition from 2D to 1D occurs at higher temperatures when the channel width is reduced to approximately 0.1 mu m. Conductivity corrections in 1D are found to be very large, so that a complete separation of interaction and localisation contributions is not possible. The current perturbation theories of interaction and localisation are therefore inadequate to explain these results.

The quantised Hall conductance alpha _xy in strong magnetic fields due to electrons in a periodic two-dimensional potential has been studied using the linear response theory. This study reveals the connection of quantised values of alpha _xy with the parameters of electron energy spectrum. The effect of the magnetic field strength and of the number of electrons has also been established.

The author derives the spin evolution equation of a classical inhomogeneous Heisenberg chain and proves its exact equivalence (in the continuum limit) to an integro-differential nonlinear Schrodinger equation whose soliton solutions have been discussed earlier. Energy transport along the chain is related to the solution of this equation. He also describes possible physical systems to which the model is applicable.

The m-magnon bound state (or soliton) excitation spectrum of an exactly solvable generalisation of the Heisenberg spin chain with arbitrary S is described. It is in qualitative agreement with predictions based on the classical continuum model. The classical limit of the generalised model is obtained.

An expression for the spin-wave stiffness coefficient D for a random one-dimensional ferromagnet is derived. It is found that D^-1=2(1/J), with J the exchange coupling constant. This coefficient vanishes in the case of a singular probability distribution of the coupling constants, implying the absence of spin waves in this case.

The object of this paper is the study of the intermolecular correlations in the orientationally disordered phases of the adamantane derivatives. The influence of the steric repulsions on the formation of the crystalline field and the occurrence of correlations is specified. A method is proposed for calculating the static susceptibility X(q) and the elastic diffuse scattering of neutrons. This enables the author to take into account the strong repulsions at the mean-field level of approximation. The theoretical prediction of the neutron pattern thus obtained is in good agreement with the experiments on plastic cyanoadamantane.

Neutron inelastic scattering experiments have been carried out to measure the phonon energies of deuterated anthracene C₁₄D₁₀ for the lowest 16 dispersion branches along (0, 0, xi ) direction at various temperatures ranging from 14 to 250K. The results for the temperature dependence of the phonon energy shift and width are presented. The phonon energies show a negative shift with increasing temperatures. A quasiharmonic treatment using Kitaigorodsky potential parameters is found to explain quite well the observed shift for some of the phonons. For the remaining phonons the measurements indicate a positive shift due to the explicit anharmonic contribution. For these phonons the magnitude of the observed widths is also large.

Building on the measured values of two librational frequencies and the tunnelling splitting, the authors determine the rotational potential of the ammonium ion in (NH₄)₂SnCl₆. Predictions are made concerning the excitations of the deuterated ammonium ion in the same crystal. A comparison with other methods shows a general agreement with respect to the pronounced anharmonicity of the potential.

Recently Yeomans and Fisher (1982) established the existence of two infinite sequences of commensurate phases near the multiphase point of the p-state asymmetric clock model for p=3. In this paper the author describes the low-temperature behaviour of the model for general p showing that, as p increases, new stable phases appear in a surprisingly regular manner. The results are obtained using a technique developed by Fisher and Selke (1981) which uses the ideas of linear programming theory to extend low-temperature series expansions to indefinitely high order.

Electrical conductivity, coulometric, DTA and DSC studies are made of orthorhombic N₂H₆SO₄ single crystals. The conductivity plot and the DTA and DSC thermograms show a phase transition at 483K, which exhibits thermal hysteresis. During cooling a multiplet structure is observed in the DSC thermogram. Activation energies obtained from the conductivity reveal that protons may be the charge carriers. This is confirmed by hydrogen gas being evolved at the cathode of the coulometer; this is analysed by gas chromatography.

Complete vibrational spectra (Raman, infrared and far-infrared) have been recorded for the ferroelastic, ferroelectric langbeinites, K₂Mn₂(SO₄)₃, (NH₄)₂Cd₂(SO₄)₃ and Tl₂Cd₂(SO₄)₃. From the polarised single-crystal Raman spectra the vibrational modes, corresponding to the 'internal' vibrations of SO₄^2-ion, were identified and assigned to the various symmetry species of the para phase factor group T for all the crystals. Single-crystal Raman spectra at various temperatures (down to liquid nitrogen temperature) were recorded to study the phase transitions. No soft modes could be observed near the phase transitions. On the other hand abrupt changes in the slopes of full width at half maximum (FWHM) versus temperature and peak height versus temperature curves, corresponding to the Raman-active SO₄ 'internal' vibrations, were seen near the phase transitions. This indicates strongly the probability of an order-disorder phase transition mechanism involving the SO₄^2- ions. Further cell doubling due to the antiferrodistortive transition to the ferroelectric phases (P2₁ and P1) in Tl₂Cd₂(SO₄)₃, which should be associated with Raman line splittings, could not be observed.

Several INDO calculations of the electronic structure of pure LiF crystal were performed in order to investigate the dependence of predicted crystalline properties upon the parameters used in the method. A new parametrisation scheme is proposed for ionic crystals.

This paper reports photoconductivity measurements of semi-insulating Ni-doped GaP materials. The photoresponse spectra obtained exhibit strong onsets at 0.62 eV and 0.95 eV, as well as a number of weaker features. Optical transitions are interpreted as between Ni³⁺ and Ni²⁺ ions, and the conduction and valence bands, as well as transitions involving a nickel-related defect. An energy diagram (at 300K) is deduced to consist of an Ni²⁺ ground state at 0.62 eV above the valence band and three excited states, and a nickel-related level located at 0.95 eV above the valence band. Optical absorption measurements have shown that the Ni⁺ two-electron trap concentration is negligible in semi-insulating GaP materials and increases appreciably under white light illumination.

The effect of electron-electron collisions with small energy transfers on the quantum electron localisation has been studied. It is shown that in one and two dimensions such collisions determine the temperature dependence of the conductivity. In three dimensions the contribution of processes with small energy transfers is less than that of the usual electron-electron collisions, in which the energy transfer is of the order of the temperature T. The criterion for the quasiparticle description of electrons in metals in different dimensions is discussed. It is shown that for d>or=2 this description is valid, while for d=1 it is not correct. The effect of noise in the external circuit on quantum corrections to the conductivity is studied.

A calculation is made of the effect on the critical temperature of a ferromagnet whose exchange integrals are taken to be random variables. The Bethe-Peierls-Weiss approximation is used to find the partition function, Z, for an Ising system and then a configuration average is taken to find (InZ), from which the resulting decrease in the critical temperature can be found. Other results are discussed and comparisons made with the present result.

The authors present the derivation of a non-linear Schrodinger equation for the quantum isotropic Heisenberg chain using the coherent-states method combined with the Holstein-Primakoff bosons representation of the spin operator. The solution of this equation gives rise to solitary-waves excitations of the system that are similar to those discussed by Tjon and Wright (1977) for the classical Heisenberg chain. A discussion of their results as compared with others in the literature is made.

The scattering of two-dimensional electrons forming a Wigner crystal by vibrations of a medium (semiconductor or liquid helium) is considered. A method is developed that gives explicit expressions (including essential corrections to the Born approximation) for the cyclotron resonance (CR) peak shape. The halfwidth and shift of the peak are analysed in detail for the cases of relatively low and high electron densities (or, respectively, strong and weak magnetic fields). The results show that at low densities CR may be used to detect the short-range order in the electron system, while at high densities the transverse sound velocity may be determined for the Wigner crystal. The theory describes quantitatively the specific dependences of the CR parameters on the electron density observed experimentally for electrons above the liquid helium surface.

The orientation dependence of W₂/W₁ for ²³Na in NaNO₂ has been measured at room temperature by a CW double-resonance method. With the exception of one point, the data are in very good agreement with the general theoretical orientation dependence. The following ratios of the M-tensor components are given by the theoretical fit: M₁₁₃₃/M₁₁₁₁=-0.890+or-0.005, M₃₃₃₃/M₁₁₁₁=1.498+or-0.031, M₂₃₂₃/M₁₁₁₁=0.076+or-0.004, M₃₁₃₁/M₁₁₁₁=0.279+or-0.011, M₁₂₁₂/M₁₁₁₁=0.200+or-0.007. These ratios are in poor agreement with those calculated for lattice vibrations, indicating that this is not the primary relaxation mechanism at room temperature. Calculated ratios of the M-tensor components associated with reorienting NO₂ groups are also in poor agreement with experiment. The theory presented in the paper is used to interpret the orientation and temperature dependence of W₁+W₂ for ²³Na in NaNO₂ reported previously by Bonera, Borsa and Rigamonti (1970). It is deduced that (M₁₁₃₃/M₁₁₁₁)² approaches M₃₃₃₃/M₁₁₁₁ near the ferroelectric phase transition, indicating a high degree of correlation between the fluctuations in V_xx and V_zz. This is what would be expected if reorienting NO₂ groups provide the dominant relaxation mechanism near the phase transition.

This paper is the first of a series addressing the macroscopic surface properties of the simple metals (the alkalis, Mg, Zn, Al, Pb) using pseudopotential perturbation theory to include the effects of discrete ions beyond the first-order Lang-Kohn jellium calculation. Here the authors give explicit formulae for the self-consistently screened inhomogeneous electron susceptibility chi (q//, z, z') calculated around the jellium surface results of Lang and Kohn (1970). In terms of chi they then give explicit formulae, up to second order in the ionic pseudopotentials, for: (i) the energy of a bounded metal; (ii) the effective ion and ion-ion potentials near a surface; (iii) the unreconstructed surface formation energy sigma at T=0K; (iv) the surface dynamical matrix; (v) the relaxation of ionic layer positions due to the surface; (vi) approximate T not=0K contributions to the surface free energy in the solid phase. As tested on face-dependent surface energies, their second-order method is a decided improvement on first-order theories, and on one-dimensional variational theories. It has a further advantage over variational approaches in that expressions for (iv), (v) and (vi) can be given in analytic form.