An application of the natural area concept to East London apartment areas

The world is faced with a population explosion, and cities are becoming ever larger. The world population will grow from its present 3500 million to more than 7 000 million by the year 2 000. The majority of cities are thus faced with the problem of housing vast numbers of people living in single family dwellings forming low density urban sprawl. Conditions are no different in South Africa where the present white population of about four million is expected to grow to between six and seven million by the year 2000. The present housing requirement (1970-75) for Whites, based on low and high population projections, is 32 732 and 40 150 houses respectively. From 1995-2000 the figures will have risen to 42 742 and 65 580 respectively. At that rate sprawl here will reach alarming proportions unless it can be curtailed by higher density housing. As the population trend does not seem likely to be reversed the problem lies in how to provide housing for an escalating population but at the same time to reduce urban sprawl and provide satisfactory living conditions

Electronic Ladders with SO(5) Symmetry: Phase Diagrams and Correlations at half-filling

We construct a family of electronic ladder models with SO(5) symmetry which have exact ground states in the form of finitely correlated wave functions. Extensions for these models preserving this symmetry are studied using these states in a variational approach. Within this approach, the zero temperature phase diagram of these electronic ladders at half filling is obtained, reproducing the known results in the weak coupling (band insulator) and strong coupling regime, first studied by Scalapino, Zhang and Hanke. Finally, the compact form of the variational wave functions allows to compute various correlation functions for these systems.Comment: RevTeX+epsf macros, 23 pp. including figure

Low Temperature Properties of Quantum Antiferromagnetic Chains with Alternating Spins S=1 and 1/2

We study the low-temperature properties of S=1 and 1/2 alternating spin chains with antiferromagnetic nearest-neighbor exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed by perturbation theory in the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations and it turns out that spin-wave theory well describes the present system. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.Comment: 13 pages, RevTeX, six figures, submitted to J. Phys. Cond. Ma

Magnetization Plateau in the Frustrated Spin Ladder

The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.Comment: 9 pages, 9 figures, other comment

Magnetic Properties of a Quantum Ferrimagnet: NiCu(pba)(D_2O)_3 . 2D_2O

We report the results of magnetic measurements on a powder sample of NiCu(pba)(D_2O)_3 \cdot 2D_2O$(pba=1,3-propylenebis(oxamato)) which is one of the prototypical examples of an$S$=1/2 and 1 ferrimagnetic chain. Susceptibility($\chi$) shows a monotonous increase with decreasing temperature (T) and reaches a maximum at about 7 K. In the plot of$\chi T$versus$T$, the experimental data exhibit a broad minimum and are fit to the$\chi T$curve calculated for the ferrimagnetic Heisenberg chain composed of S=1/2 and 1. From this fit, we have evaluated the nearest-neighbor exchange constant$J/k_B=121 K$, the g-values of Ni$^{2+}$and Cu$^{2+}$,$g_{Ni}$=2.22 and$g_{Cu}$=2.09, respectively. Applied external field dependence of$\chi T$ at low temperatures is reproduced fairly well by the calculation for the same ferrimagnetic model.Comment: 7pages, 4 postscript figures, usues REVTEX. appear in J. Phys. Soc. Jpn vol 67 No.7 (1998

Dynamical structure factors of S=1/2S=1/2 two-leg spin ladder systems

We investigate dynamical properties of $S=1/2$ two-leg spin ladder systems. In a strong coupling region, an isolated mode appears in the lowest excited states, while in a weak coupling region, an isolated mode is reduced and the lowest excited states become a lower bound of the excitation continuum. We find in the system with equal intrachain and interchain couplings that due to a cyclic four-spin interaction, the distribution of the weights for the dynamical structure factor and characteristics of the lowest excited states are strongly influenced. The dynamical properties of two systems proposed for ${\rm SrCu_2O_3}$ are also discussed.Comment: 5 pages, 6 figure

Spin-dependent resonant tunneling through semimetallic ErAs quantum wells

Resonant tunneling through semimetallic ErAs quantum wells embedded in GaAs structures with AlAs barriers was recently found to exhibit an intriguing behavior in magnetic fields which is explained in terms of tunneling selection rules and the spin-polarized band structure including spin-orbit coupling.Comment: 4 pages, figures supplied as self-unpacking figures.uu, uses epsfig.sty to incorporate figures in preprin

Mixed Heisenberg Chains. I. The Ground State Problem

We consider a mechanism for competing interactions in alternating Heisenberg spin chains due to the formation of local spin-singlet pairs. The competition of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating chains.Comment: 7 pages, RevTeX, 4 embedded eps figures, final versio

Exact symmetry breaking ground states for quantum spin chains

We introduce a family of spin-1/2 quantum chains, and show that their exact ground states break the rotational and translational symmetries of the original Hamiltonian. We also show how one can use projection to construct a spin-3/2 quantum chain with nearest neighbor interaction, whose exact ground states break the rotational symmetry of the Hamiltonian. Correlation functions of both models are determined in closed form. Although we confine ourselves to examples, the method can easily be adapted to encompass more general models.Comment: 4 pages, RevTex. 4 figures, minor changes, new reference

Low-Energy Structure of Heisenberg Ferrimagnetic Spin Chains

Static and dynamic structure factors of Heisenberg ferrimagnetic spin chains are numerically investigated. There exist two distinct branches of elementary excitations, which exhibit ferromagnetic and antiferromagnetic aspects. The ferromagnetic feature is smeared out with the increase of temperature, whereas the antiferromagnetic one persists up to higher temperatures. The scattering intensity is remarkably large at lower boundaries of the ferromagnetic and antiferromagnetic spectra. All these observations are consistent with the ferromagnetic-to-antiferromagnetic crossover in the thermal behavior which has recently been reported.Comment: 3 pages, 5 PS figures, to appear in J. Phys. Soc. Jpn. Vol. 67, No. 11 (1998