Momentum dependent light scattering in insulating cuprates

We investigate the problem of inelastic x-ray scattering in the spin$-{1/2}$ Heisenberg model on the square lattice. We first derive a momentum dependent scattering operator for the $A_{1g}$ and $B_{1g}$ polarization geometries. On the basis of a spin-wave analysis, including magnon-magnon interactions and exact-diagonalizations, we determine the qualitative shape of the spectra. We argue that our results may be relevant to help interpret inelastic x-ray scattering experiments in the antiferromagnetic phase of the cuprates.Comment: 5 pages, 3 figures, to appear in PR

Magnetic charge and ordering in kagome spin ice

We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbors, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz-Thouless transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high and low-temperature phase transitions are of the Ising and 3-state Potts universality classes, respectively. Freeze-out of defects in the charge order produces a very large spin correlation length in the intermediate phase. As a result of that, the lower-temperature transition appears to be of the Kosterlitz-Thouless type.Comment: 20 pages, 12 figures, accepted version with minor change

Ferroelectric and Dipolar Glass Phases of Non-Crystalline Systems

In a recent letter [Phys. Rev. Lett. {\bf 75}, 2360 (1996)] we briefly discussed the existence and nature of ferroelectric order in positionally disordered dipolar materials. Here we report further results and give a complete description of our work. Simulations of randomly frozen and dynamically disordered dipolar soft spheres are used to study ferroelectric ordering in non-crystalline systems. We also give a physical interpretation of the simulation results in terms of short- and long-range interactions. Cases where the dipole moment has 1, 2, and 3 components (Ising, XY and XYZ models, respectively) are considered. It is found that the Ising model displays ferroelectric phases in frozen amorphous systems, while the XY and XYZ models form dipolar glass phases at low temperatures. In the dynamically disordered model the equations of motion are decoupled such that particle translation is completely independent of the dipolar forces. These systems spontaneously develop long-range ferroelectric order at nonzero temperature despite the absence of any fined-tuned short-range spatial correlations favoring dipolar order. Furthermore, since this is a nonequilibrium model we find that the paraelectric to ferroelectric transition depends on the particle mass. For the XY and XYZ models, the critical temperatures extrapolate to zero as the mass of the particle becomes infinite, whereas, for the Ising model the critical temperature is almost independent of mass and coincides with the ferroelectric transition found for the randomly frozen system at the same density. Thus in the infinite mass limit the results of the frozen amorphous systems are recovered.Comment: 25 pages (LATEX, no macros). 11 POSTSCRIPT figures enclosed. Submitted to Phisical Review E. Contact: [email protected]

Experimental Predictions of The Functional Response of A Freshwater Fish

The functional response is the relationship between the feeding rate of an animal and its food density. It is reliant on two basic parameters; the volume searched for prey per unit time (searching rate) and the time taken to consume each prey item (handling time). As fish functional responses can be difficult to determine directly, it may be more feasible to measure their underlying behavioural parameters in controlled conditions and use these to predict the functional response. Here, we tested how accurately a Type II functional response model predicted the observed functional response of roach Rutilus rutilus, a visually foraging fish, and compared it with Type I functional response. Foraging experiments were performed by exposing fish in tank aquaria to a range of food densities, with their response captured using a two-camera videography system. This system was validated and was able to accurately measure fish behaviour in the aquaria, and enabled estimates of fish reaction distance, swimming speed (from which searching rate was calculated) and handling time to be measured. The parameterised Type II functional response model accurately predicted the observed functional response and was superior to the Type I model. These outputs suggest it will be possible to accurately measure behavioural parameters in other animal species and use these to predict the functional response in situations where it cannot be observed directly

Artificial Kagome Arrays of Nanomagnets: A Frozen Dipolar Spin Ice

Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and Monte Carlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails.Comment: 4 pages, 4 figures, 1 tabl

Glassiness Vs. Order in Densely Frustrated Josephson Arrays

We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first order equilibrium phase transition to an ordered vortex structure at a T_c which varies only slightly with f. This ordered vortex structure remains in general phase incoherent until a lower pinning transition T_p(f) that varies with f. We argue that the glassy behaviors reported for this model in earlier simulations are dynamic effects.Comment: 4 pages, 4 eps figure

Fractal Droplets in Two Dimensional Spin Glasses

The two-dimensional Edwards-Anderson model with Gaussian bond distribution is investigated at T=0 with a numerical method. Droplet excitations are directly observed. It turns out that the averaged volume of droplets is proportional to l^D with D = 1.80(2) where l is the spanning length of droplets, revealing their fractal nature. The exponent characterizing the l dependence of the droplet excitation energy is estimated to be -0.42(4), clearly different from the stiffness exponent for domain wall excitations.Comment: 4 pages 4 figure

Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material

Spin ices, frustrated magnetic materials analogous to common water ice, are exemplars of high frustration in three dimensions. Recent experimental studies of the low-temperature properties of the paradigmatic Dy$_2$Ti$_2$O$_7$ spin ice material, in particular whether the predicted transition to long-range order occurs, raise questions as per the currently accepted microscopic model of this system. In this work, we combine Monte Carlo simulations and mean-field theory calculations to analyze data from magnetization, elastic neutron scattering and specific heat measurements on Dy$_2$Ti$_2$O$_7$. We also reconsider the possible importance of the nuclear specific heat, $C_{\rm nuc}$, in Dy$_2$Ti$_2$O$_7$. We find that $C_{\rm nuc}$ is not entirely negligible below a temperature $\sim 0.5$ K and must be taken into account in a quantitative analysis of the calorimetric data of this compound below that temperature. We find that small effective exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected "refrustration" of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range ordered ground states. This allows for the manifestation of new physical low-temperature phenomena in Dy$_2$Ti$_2$O$_7$, as exposed by recent specific heat measurements. We show that among the four most likely causes for the observed upturn of the specific heat at low temperature -- an exchange-induced transition to long-range order, quantum non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear hyperfine contribution and random disorder -- only the last appears to be reasonably able to explain the calorimetric data.Comment: 24 pages, 18 figures. To appear in Physical Review