Scaling of loop-erased walks in 2 to 4 dimensions

We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2,3, and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in $d=4$, simulations in lower dimensions were done for completeness and in order to test the algorithm. In $d=2$, we verify with high precision the prediction $D=5/4$, where the number of steps $n$ after erasure scales with the number $N$ of steps before erasure as $n\sim N^{D/2}$. In $d=3$ we again find a power law, but with an exponent different from the one found in the most precise previous simulations: $D = 1.6236\pm 0.0004$. Finally, we see clear deviations from the naive scaling $n\sim N$ in $d=4$. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect.Comment: 3 pages, including 3 figure

A closer look at symmetry breaking in the collinear phase of the J1−J2J_1-J_2 Heisenberg Model

The large $J_2$ limit of the square-lattice $J_1-J_2$ Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a meanfield spin-wave theory to study the excitation spectra in this phase and look for a finite temperature Ising-like transition, corresponding to a broken symmetry of the square-lattice, as first proposed by Chandra et al. (Phys. Rev. Lett. 64, 88 (1990)). We find that the spectra reveal the symmetries of the ordered phase. However, we do not find any evidence for a finite temperature phase transition. Based on an effective field theory we argue that the Ising-like transition occurs only at zero temperature.Comment: 4 pages and 5 figure

Outcomes following the surgical management of left ventricular outflow tract obstruction; A systematic review and meta-analysis

BACKGROUND: Left ventricular outflow tract obstruction (LVOTO) causes exertional symptoms in two thirds of patients with hypertrophic cardiomyopathy (HCM). Consensus guidelines recommend surgical intervention in patients with drug refractory symptoms. The primary aim of this study was to perform a systematic review and meta-analysis to determine morbidity and mortality after surgery. METHODS: Study Selection: Studies reporting outcomes following surgical intervention for symptomatic LVOTO in HCM. RESULTS: 85 studies were included in the systematic review and 35 studies in the meta-analysis. Contemporary early (30 days) mortality following septal myectomy were 1.4% (CI 0.8, 2.4) I^{2} 9.0%, p = 0.36 and 0.7% (CI 0.3, 1.2) I^{2} 70.7%, p < 0.05 respectively. Sixty-eight studies (80%) reported perioperative complications. The contemporary rate of a perioperative ventricular septal defect was 1.4% (0.8, 2.3) I^{2} 0%, p < 0.05. Late morbidities including atrial fibrillation, stroke, heart failure and transplant were reported in fewer than 22% of studies and few studies compared mortality and clinical outcomes using different surgical approaches to LVOTO. The incidence rate (IR) of reintervention with a further surgical procedure was 0.3% (CI 0.2, 0.4) I^{2} 52.5%, p < 0.05. CONCLUSIONS: Contemporary surgical management of LVOTO is associated with low operative mortality rates but further studies are needed to investigate the impact of surgical therapy on non-fatal early and late complications

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Cognitive Information Processing

Contains reports on five research projects.National Institutes of Health (Grant 5 PO1 GM-14940-02)National Institutes of Health (Grant 5 P01 GM-15006-02)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Cognitive Information Processing

Contains reports on six research projects.National Institutes of Health (Grant 5 PO1 GM14940-03)National Institutes of Health (Grant 5 PO1 GM15006-03)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E)National Institutes of Health (Grant 5 TO1 GM01555-03

Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution

We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus on the problem of reproducing the parametrization corresponding to that of lattice models, namely self-avoiding walks on the lattice, and we propose a strategy that gives rise to discrete paths where consecutive points lie an approximately constant distance apart from each other. This new method allows us to tackle two non-trivial features of self-avoiding walks that critically depend on the parametrization: the asphericity of a portion of chain and the correction-to-scaling exponent.Comment: 18 pages, 4 figures. Some sections rewritten (including title and abstract), numerical results added, references added. Accepted for publication in J. Stat. Phy

New quantum phase transitions in the two-dimensional J1-J2 model

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the J1-J2 model, in two dimensions. Two quantum phase transitions in the model are already known: the second order transition from the Neel state to the spin liquid state at (J_2/J_1)_{c2}=0.38, and the first order transition from the spin liquid state to the collinear state at (J_2/J_1)_{c4}=0.60. We have found evidence for two new second order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette type modulation at (J_2/J_1)_{c3}=0.50(2), and the transition from the simple Neel state to the Neel state with spin columnar dimerization at (J_2/J_1)_{c1}=0.34(4). We also present an independent calculation of (J_2/J_1)_{c2}=0.38 using a new approach.Comment: 3 pages, 5 figures; added referenc

Hyperuniversality of Fully Anisotropic Three-Dimensional Ising Model

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by the transfer-matrix method and a finite-size scaling for cyclic L x L x oo clusters with L=3 and 4. Analysis of the data obtained shows that the ratios and the directional geometric means of above amplitudes are universal.Comment: RevTeX 3.0, 24 pages, 2 figures upon request, accepted for publication in Phys. Rev.

Determination of two-photon exchange amplitudes from elastic electron-proton scattering data

Using the available cross section and polarization data for elastic electron-proton scattering, we provide an extraction of the two-photon exchange amplitudes at a common value of four-momentum transfer, around Q^2 = 2.5 GeV^2. This analysis also predicts the e^+ p / e^- p elastic scattering cross section ratio, which will be measured by forthcoming experiments.Comment: 4 pages, 5 figures, updated error analysi