496 research outputs found
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
, simulations in lower dimensions were done for completeness and in order
to test the algorithm. In , we verify with high precision the prediction
, where the number of steps after erasure scales with the number
of steps before erasure as . In we again find a power law,
but with an exponent different from the one found in the most precise previous
simulations: . Finally, we see clear deviations from the
naive scaling in . 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 Heisenberg Model
The large limit of the square-lattice 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
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