The Ising phase in the J1-J2 Heisenberg Model

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.Comment: 6 pages, 4 figures, to be published in PR

Fractional Spin for Quantum Hall Effect Quasiparticles

We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=\theta/2\pi$, with $\theta$ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. By performing Berry-phase calculations for quasiparticles on a sphere we find that there are two terms, of different origin, that couple to the curvature and can be interpreted as parts of the quasiparticle spin. One, due to self-interaction, has the same value for both the quasihole and quasielectron, and fulfills the spin-statistics relation. The other is a kinematical effect and has opposite signs for the quasihole and quasielectron. The total spin thus agrees with a generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = \theta/2\pi$. On the plane, we do not find any corresponding terms.Comment: 15 pages, RevTeX-3.

Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Pad\'e approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with $\alpha (= J_2/J_1)$. The spin-gap phase persists down to $J_3=0$ (single layer limit) for 0.45 \simleq \alpha \simleq 0.65. The crossover of the short range order within the disordered phase is also discussed.Comment: 4 pages, 6 figures, One reference adde

Topological orders and Edge excitations in FQH states

Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss characterization and classification of the new orders (which is called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very rich structures as a reflection of the rich topological orders in the bulk. Thus, edge excitations provide us a practical way to measure topological orders in experiments.Comment: 67 pages, plain-tex, 3 figures. The section about spin vector was rewritten to make it more readabl

Individual risk assessment and information technology to optimise screening frequency for diabetic retinopathy.

To access publisher full text version of this article. Please click on the hyperlink in Additional Links field.AIMS/HYPOTHESIS: The aim of this study was to reduce the frequency of diabetic eye-screening visits, while maintaining safety, by using information technology and individualised risk assessment to determine screening intervals. METHODS: A mathematical algorithm was created based on epidemiological data on risk factors for diabetic retinopathy. Through a website, www.risk.is , the algorithm receives clinical data, including type and duration of diabetes, HbA(1c) or mean blood glucose, blood pressure and the presence and grade of retinopathy. These data are used to calculate risk for sight-threatening retinopathy for each individual's worse eye over time. A risk margin is defined and the algorithm recommends the screening interval for each patient with standardised risk of developing sight-threatening retinopathy (STR) within the screening interval. We set the risk margin so that the same number of patients develop STR within the screening interval with either fixed annual screening or our individualised screening system. The database for diabetic retinopathy at the Department of Ophthalmology, Aarhus University Hospital, Denmark, was used to empirically test the efficacy of the algorithm. Clinical data exist for 5,199 patients for 20 years and this allows testing of the algorithm in a prospective manner. RESULTS: In the Danish diabetes database, the algorithm recommends screening intervals ranging from 6 to 60 months with a mean of 29 months. This is 59% fewer visits than with fixed annual screening. This amounts to 41 annual visits per 100 patients. CONCLUSION: Information technology based on epidemiological data may facilitate individualised determination of screening intervals for diabetic eye disease. Empirical testing suggests that this approach may be less expensive than conventional annual screening, while not compromising safety. The algorithm determines individual risk and the screening interval is individually determined based on each person's risk profile. The algorithm has potential to save on healthcare resources and patients' working hours by reducing the number of screening visits for an ever increasing number of diabetic patients in the world

Modified Spin Wave Thoery of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest and next-nearest neighbour intralayer interaction is studied by means of the modified spin wave method. For weak interlayer coupling, the ground state is found to be always magnetically ordered while the quantum disordered phase appear for large enough interlayer coupling. The properties of the disordered phase vary according to the strength of the frustration. In the regime of weak frustration, the disordered ground state is an almost uncorrelated assembly of interlayer dimers, while in the strongly frustrated regime the quantum spin liquid phase which has considerable N\'eel type short range order appears. The behavior of the sublattice magnetization and spin-spin correlation length in each phase is discussed.Comment: 15 pages, revtex, figures upon reques

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 figure

Meissner effect in honeycomb arrays of multi-walled carbon nanotubes

We report Meissner effect for type-II superconductors with a maximum Tc of 19 K, which is the highest value among those in new-carbon related superconductors, found in the honeycomb arrays of multi-walled CNTs (MWNTs). Drastic reduction of ferromagnetic catalyst and efficient growth of MWNTs by deoxidization of catalyst make the finding possible. The weak magnetic anisotropy, superconductive coherence length (- 7 nm), and disappearance of the Meissner effect after dissolving array structure indicate that the graphite structure of an MWNT and those intertube coupling in the honeycomb array are dominant factors for the mechanism.Comment: 6 page

Individualised risk assessment for diabetic retinopathy and optimisation of screening intervals: a scientific approach to reducing healthcare costs.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.To validate a mathematical algorithm that calculates risk of diabetic retinopathy progression in a diabetic population with UK staging (R0-3; M1) of diabetic retinopathy. To establish the utility of the algorithm to reduce screening frequency in this cohort, while maintaining safety standards.The cohort of 9690 diabetic individuals in England, followed for 2 years. The algorithms calculated individual risk for development of preproliferative retinopathy (R2), active proliferative retinopathy (R3A) and diabetic maculopathy (M1) based on clinical data. Screening intervals were determined such that the increase in risk of developing certain stages of retinopathy between screenings was the same for all patients and identical to mean risk in fixed annual screening. Receiver operating characteristic curves were drawn and area under the curve calculated to estimate the prediction capability.The algorithm predicts the occurrence of the given diabetic retinopathy stages with area under the curve =80% for patients with type II diabetes (CI 0.78 to 0.81). Of the cohort 64% is at less than 5% risk of progression to R2, R3A or M1 within 2 years. By applying a 2 year ceiling to the screening interval, patients with type II diabetes are screened on average every 20 months, which is a 40% reduction in frequency compared with annual screening.The algorithm reliably identifies patients at high risk of developing advanced stages of diabetic retinopathy, including preproliferative R2, active proliferative R3A and maculopathy M1. Majority of patients have less than 5% risk of progression between stages within a year and a small high-risk group is identified. Screening visit frequency and presumably costs in a diabetic retinopathy screening system can be reduced by 40% by using a 2 year ceiling. Individualised risk assessment with 2 year ceiling on screening intervals may be a pragmatic next step in diabetic retinopathy screening in UK, in that safety is maximised and cost reduced by about 40%.Icelandic Research Counci