Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models

We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid (VBS) correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as $1/r^a$ with $a \approx 1.20$, compared with $a=2$ for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a "height" model characterized by a gradient-squared stiffness constant $K$. Four independent measurements consistently show a value $K_{RVB} \approx 1.6 K_{CDM}$, with the same kinds of numerical evaluations of $K_{CDM}$ give results in agreement with the rigorously known value $K_{CDM}=\pi/16$. The background of a nonzero winding number gradient $W/L$ introduces spatial anisotropies and an increase in the effective K, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of "Cantor deconfinement" in extended quantum dimer models. We also study ensembles in which fourth-neighbor (bipartite) bonds are allowed, at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of K.Comment: 26 pages, 21 figures. v3: final versio

Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach

Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagom\'e lattice has long-range spin order of the $\sqrt{3}\times\sqrt{3}$ type (modulo gradual orientation fluctuations of the spins' plane). I start from the effective quartic Hamiltonian for the soft (out of plane) spin fluctuation modes, and treat as a perturbation those terms which depend on the discrete coplanar state. Soft mode correlations, which become the coefficients of a discrete effective Hamiltonian, are estimated analytically.Comment: 4pp, no figures. Converted to PRB format, extensive revisions/some reorderings to improve clarity; some cut

Probing the wind-wind collision in Gamma Velorum with high-resolution Chandra X-ray spectroscopy: evidence for sudden radiative braking and non-equilibrium ionization

We present a new analysis of an archived Chandra HETGS X-ray spectrum of the WR+O colliding wind binary Gamma Velorum. The spectrum is dominated by emission lines from astrophysically abundant elements: Ne, Mg, Si, S and Fe. From a combination of broad-band spectral analysis and an analysis of line flux ratios we infer a wide range of temperatures in the X-ray emitting plasma (~4-40 MK). As in the previously published analysis, we find the X-ray emission lines are essentially unshifted, with a mean FWHM of 1240 +/- 30 km/s. Calculations of line profiles based on hydrodynamical simulations of the wind-wind collision predict lines that are blueshifted by a few hundred km/s. The lack of any observed shift in the lines may be evidence of a large shock-cone opening half-angle (> 85 degrees), and we suggest this may be evidence of sudden radiative braking. From the R and G ratios measured from He-like forbidden-intercombination-resonance triplets we find evidence that the Mg XI emission originates from hotter gas closer to the O star than the Si XIII emission, which suggests that non-equilibrium ionization may be present.Comment: 22 pages, 14 figures. Accepted for publication in MNRA

Hot Gas in the Galactic Thick Disk and Halo Near the Draco Cloud

This paper examines the ultraviolet and X-ray photons generated by hot gas in the Galactic thick disk or halo in the Draco region of the northern hemisphere. Our analysis uses the intensities from four ions, C IV, O VI, O VII, and O VIII, sampling temperatures of ~100,000 to ~3,000,000 K. We measured the O VI, O VII and O VIII intensities from FUSE and XMM-Newton data and subtracted off the local contributions in order to deduce the thick disk/halo contributions. These were supplemented with published C IV intensity and O VI column density measurements. Our estimate of the thermal pressure in the O VI-rich thick disk/halo gas, p_{th}/k = 6500^{+2500}_{-2600} K cm^{-3}, suggests that the thick disk/halo is more highly pressurized than would be expected from theoretical analyses. The ratios of C IV to O VI to O VII to O VIII, intensities were compared with those predicted by theoretical models. Gas which was heated to 3,000,000 K then allowed to cool radiatively cannot produce enough C IV or O VI-generated photons per O VII or O VIII-generated photon. Producing enough C IV and O VI emission requires heating additional gas to 100,000 < T < 1,000,000 K. However, shock heating, which provides heating across this temperature range, overproduces O VI relative to the others. Obtaining the observed mix may require a combination of several processes, including some amount of shock heating, heat conduction, and mixing, as well as radiative cooling of very hot gas.Comment: 10 pages, 2 figures. Accepted for publication in the Astrophysical Journa

Tensions in setting health care priorities for South Africa's children.

The new South African constitution commits the government to guarantee "basic health services "for every child under 18. Primary health care for pregnant women and children under six and elements of essential primary health care have received priority. At present, there is little analysis of the moral considerations involved in making choices about more advanced or costly health care which may, arguably, also be "basic". This paper illustrates some of the tensions in setting priorities for a just macroallocation of children's health care, given the realities of need and scarce resources, and the commitment to equality of basic opportunities. Originally published Journal of Medical Ethics, Vol. 24, No. 4, Aug 199

First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural disorder corresponds to phason (tile flip) fluctuations. First-principles total energy calculations reveal that many distinct tilings lie close to stability at low temperatures. Transfer matrix calculations based on these energies suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is metastable at low temperatures and may be thermodynamically stable at high temperatures.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Flip dynamics in octagonal rhombus tiling sets

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size $N_T$ like $Cst. N_T^2 \ln N_T$; these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.Comment: 5 Revtex pages, 4 figures; definitive versio

Method of fabricating an object with a thin wall having a precisely shaped slit

A method is described for making a structure with a cavity and a thin wall with a precisely shaped slit. An object with a cavity having two openings, one of which is to be closed by a thin wall with a slit, is placed on the surface of a fixture. The fixture surface has a slot conforming to the size and shape of the slit to be formed in the thin wall

Spin of ground state baryons

We calculate the quark spin contribution to the total angular momentum of flavor octet and flavor decuplet ground state baryons using a spin-flavor symmetry based parametrization method of quantum chromodynamics. We find that third order SU(6) symmetry breaking three-quark operators are necessary to explain the experimental result Sigma_1=0.32(10). For spin 3/2 decuplet baryons we predict that the quark spin contribution is Sigma_3=3.93(22), i.e. considerably larger than their total angular momentum.Comment: 8 page