Komajiro Niizeki

Monte Carlo Simulation of the Ising Model on the Penrose Lattice

The critical properties of the Ising model on the Penrose lattice of a size up to 439,204 sites are studied by means of the Monte Carlo simulation. We make an analysis of a phenomenological Monte Carlo renormalization group based on finite-size scaling. The critical temperature T c and the magnetic critical exponent y H are obtained to be (2.392±0.004) J and 1.89±0.02. The value of y H coincides with the value of a two-dimensional crystal, y H =1.875, within numerical accuracy.

Special points in the reciprocal space of an icosahedral quasi-crystal and the quasi-dispersion relation of electrons

It is shown that there exist special points in the reciprocal space of an icosahedral quasi-lattice; they correspond to high-symmetry points in the Brillouin zone of a periodic lattice. The translationally equivalent special points are distributed quasi-periodically with different intensities in the reciprocal space. On the other hand, electronic wavefunctions of the icosahedral quasi-lattice are investigated using a numerical method based on the tight-binding model. Their Fourier spectra are mapped in the energy versus wavenumber plane along several axes in reciprocal space. Dispersion-relation-like patterns are observed. It is found that critical points (stationary points) of the quasi-dispersion relation appear at the special points. The quasi-dispersion relation recurs quasi-periodically all over reciprocal space.

The band structure of solid iodine under pressure and the mechanism of the pressure-induced insulator-to-metal transition

The band structures of solid iodine under ambient pressure and 15.3 GPa were calculated with the ab initio pseudopotential method. The apparently complicated band structures have been resolved by a detailed analysis, revealing the mechanism of the band overlap which causes the pressure-induced insulator-to-metal transition: The interlayer interaction as well as the interaction between the third-nearest neighbor atoms is responsible for the band overlap. The effect of the spin-orbit interaction on the band overlap is also discussed

A classification of special points of icosahedral quasilattices

Investigates special points of icosahedral quasilattices in three dimensions (3D). They are given as the projections onto the real space of the special points of icosahedral lattices which are periodic lattices in 6D. There exist three Bravais classes of 6D icosahedral lattices and the author present a complete classification of their special points.

CPA conductivity of a binary alloy with off-diagonal disorder

Abstract D.c.-conductivity of a binary alloy A x B y with off-diagonal disorder is calculated, assuming Shibas condition for the random transfer integrals, by means of a modified CPA, i.e.,the renormalization propagator formalism developed elsewhere by one of the authors (K.N.).

Duality in the Ising Model on the Quasicrystals

The ferromagnetic Ising model on the dual Penrose lattice is simulated by the Monte Carlo method. Using a phenomenological Monte Carlo renormalization group based on finite-size scaling, the critical temperature and the magnetic critical exponent are estimated as T c / J =2.150±0.006 and y H =1.88±0.02. It is shown that the duality relation, sinh (2 J / T c )sinh (2 J / T c * )=1, between the critical temperature of the Ising model on a lattice T c and that on its dual lattice T c * holds for a quasiperiodic lattice in two dimensions as well as for a regular lattice.

The CPA Calculation of the Thermoelectric Power of a Binary Alloy with Off-Diagonal Disorder

The thermoelectric power of a binary alloy with off-diagonal disorder as well as diagonal one is calculated by means of the extended coherent potential approximation due to Shiba and others. It is shown that the off-diagonal disorder has a very striking effect on the thermoelectric power as well as on the conductivity. In the calculation the “underturbed” band is treated accurately for a simple cubic tight-binding model. Our improved treatment of the van Hove singularities of the “unperturbed” band reveals that the effect of the singularities on the transport coefficient is more pronounced than that calculated by Levin et al.

A classification of the space groups of approximant lattices to a decagonal quasilattice

A periodic approximant to a two-dimensional (2D) decagonal quasilattice is obtained by the projection method from a 4D periodic lattice, L, which is a commensurate deformation of the 4D decagonal lattice. The Bravais lattice of the approximant is given by the restriction of L onto the physical space, while its space group by the symmetry of the phase vector with respect to the 2D lattice, Ls, which is the projection of L onto the internal space. There exist 12 space groups of the rectangular approximants, pmm, pmg, pgm, pgg, pm1, p1m, pg1, p1g, cmm( Gamma ), cmm(Y), cm1 and c1m, which are derived from the special points or special lines of Ls.

High-pressure phases of group-5B elements: Arsenic and antimony

Abstract For two group-5B elements, arsenic and antimony, the total energies of the simple cubic (sc) and body-centered cubic (bcc) structures are calculated within the local density-functional formalism and the norm-conserving pseudopotential method. Calculated equations of states for the observed high-pressure phases, the sc phase of arsenic and the bcc phase of antimony, are in excellent agreement with the experimental ones. We find that the sc phase of arsenic is stable at pressures below 70.9 GPa and that of antimony is unstable over the range of pressure where the bcc phase of antimony has been observed.

Band structure and structural stability of the high-pressure phases of the group VIb elements

Abstract The group VIb elements, such as sulfur, selenium and tellurium, exhibit similar successive structural phase transitions under pressure. The electronic band-structure of the high-pressure phases of these elements is investigated on the basis of first principles calculation. In particular, the structural stability of the β-Po type rhombohedral phase of selenium has been studied, and the result suggests that the rhombohedral structure becomes unstable owing to monoclinic distortion.