Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Spin-labeling coronary MR angiography with steady-state free precession and radial k-space sampling: initial results in healthy volunteers.

The purpose of this study was to prospectively compare free-breathing navigator-gated cardiac-triggered three-dimensional steady-state free precession (SSFP) spin-labeling coronary magnetic resonance (MR) angiography performed by using Cartesian k-space sampling with that performed by using radial k-space sampling. A new dedicated placement of the two-dimensional selective labeling pulse and an individually adjusted labeling delay time approved by the institutional review board were used. In 14 volunteers (eight men, six women; mean age, 28.8 years) who gave informed consent, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), vessel sharpness, vessel length, and subjective image quality were investigated. Differences between groups were analyzed with nonparametric tests (Wilcoxon, Pearson chi2). Radial imaging, as compared with Cartesian imaging, resulted in a significant reduction in the severity of motion artifacts, as well as an increase in SNR (26.9 vs 12.0, P < .05) in the coronary arteries and CNR (23.1 vs 8.8, P < .05) between the coronary arteries and the myocardium. A tendency toward improved vessel sharpness and vessel length was also found with radial imaging. Radial SSFP imaging is a promising technique for spin-labeling coronary MR angiography.

Free-breathing renal magnetic resonance angiography with steady-state free-precession and slab-selective spin inversion combined with radial k-space sampling and water-selective excitation.

The impact of radial k-space sampling and water-selective excitation on a novel navigator-gated cardiac-triggered slab-selective inversion prepared 3D steady-state free-precession (SSFP) renal MR angiography (MRA) sequence was investigated. Renal MRA was performed on a 1.5-T MR system using three inversion prepared SSFP approaches: Cartesian (TR/TE: 5.7/2.8 ms, FA: 85 degrees), radial (TR/TE: 5.5/2.7 ms, FA: 85 degrees) SSFP, and radial SSFP combined with water-selective excitation (TR/TE: 9.9/4.9 ms, FA: 85 degrees). Radial data acquisition lead to significantly reduced motion artifacts (P < 0.05). SNR and CNR were best using Cartesian SSFP (P < 0.05). Vessel sharpness and vessel length were comparable in all sequences. The addition of a water-selective excitation could not improve image quality. In conclusion, radial k-space sampling reduces motion artifacts significantly in slab-selective inversion prepared renal MRA, while SNR and CNR are decreased. The addition of water-selective excitation could not improve the lower CNR in radial scanning.

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

Free-breathing renal MR angiography with steady-state free-precession (SSFP) and slab-selective spin inversion: initial results.

BACKGROUND: The aim of our study was the investigation of a novel navigator-gated three-dimensional (3D) steady-state free-precession (SSFP) sequence for free-breathing renal magnetic resonance angiography (MRA) without contrast medium, and to examine the advantage of an additional inversion prepulse for improved contrast. METHODS: Eight healthy volunteers (mean age 29 years) and eight patients (mean age 53 years) were investigated on a 1.5 Tesla MR system (ACS-NT, Philips, Best, The Netherlands). Renal MRA was performed using three navigator-gated free-breathing cardiac-triggered 3D SSFP sequences [repetition time (TR) = 4.4 ms, echo time (TE) = 2.2 ms, flip angle 85 degrees, spatial resolution 1.25 x 1.25 x 4.0 mm(3), scanning time approximately 1 minute 30 seconds]. The same sequence was performed without magnetization preparation, with a non-slab selective and a slab-selective inversion prepulse. Signal-to-noise ratio (SNR), contrast-to-noise (CNR) vessel length, and subjective image quality were compared. RESULTS: Three-dimensional SSFP imaging combined with a slab-selective inversion prepulse enabled selective and high contrast visualization of the renal arteries, including the more distal branches. Standard SSFP imaging without magnetization preparation demonstrated overlay by veins and renal parenchyma. A non-slab-selective prepulse abolished vessel visualization. CNR in SSFP with slab-selective inversion was 43.6 versus 10.6 (SSFP without magnetization preparation) and 0.4 (SSFP with non-slab-selective inversion), P < 0.008. CONCLUSION: Navigator-gated free-breathing cardiac-triggered 3D SSFP imaging combined with a slab-selective inversion prepulse is a novel, fast renal MRA technique without the need for contrast media.

Optical evidence for the proximity to a spin-density-wave metallic state in Na0.7CoO2

We present the optical properties of Na0.7CoO2 single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate (Gamma) and effective mass (m*) of the itinerant charge carriers. We find that Gamma(omega) at low temperatures and for similar to omega. This suggests that Na0.7CoO2 is at the verge of a spin-density-wave metallic phase.

Ground-state order and spin-lattice coupling in tetrahedral spin systems Cu2Te2O5X2 (X = Br or Cl)

High-resolution ac susceptibility and thermal conductivity measurement on Cu2Te2O5X2 (X=Br,Cl) single crystals are reported. For Br-sample, sample dependence prevents one from distinguishing between possibilities of magnetically ordered and spin-singlet ground states. In Cl-sample a three-dimensional transition at 18.5 K is accompanied by almost isotropic behavior of susceptibility and almost switching behavior of thermal conductivity. Thermal conductivity studies suggest the presence of a tremendous spin-lattice coupling characterizing Cl- but not Br-sample. Below the transition Cl-sample is in a complex magnetic state involving AF order but also the elements consistent with the presence of a gap in the excitation spectrum.

Nonenhanced arterial spin labeled carotid MR angiography using three-dimensional radial balanced steady-state free precession imaging.

PURPOSE: To optimize and preliminarily evaluate a three-dimensional (3D) radial balanced steady-state free precession (bSSFP) arterial spin labeled (ASL) sequence for nonenhanced MR angiography (MRA) of the extracranial carotid arteries. MATERIALS AND METHODS: The carotid arteries of 13 healthy subjects and 2 patients were imaged on a 1.5 Tesla MRI system using an undersampled 3D radial bSSFP sequence providing a scan time of ∼4 min and 1 mm(3) isotropic resolution. A hybridized scheme that combined pseudocontinuous and pulsed ASL was used to maximize arterial coverage. The impact of a post label delay period, the sequence repetition time, and radiofrequency (RF) energy configuration of pseudocontinuous labeling on the display of the carotid arteries was assessed with contrast-to-noise ratio (CNR) measurements. Faster, higher undersampled 2 and 1 min scans were tested. RESULTS: Using hybridized ASL MRA and a 3D radial bSSFP trajectory, arterial CNR was maximized with a post label delay of 0.2 s, repetition times ≥ 2.5 s (P < 0.05), and by eliminating RF energy during the pseudocontinuous control phase (P < 0.001). With higher levels of undersampling, the carotid arteries were displayed in ≤ 2 min. CONCLUSION: Nonenhanced MRA using hybridized ASL with a 3D radial bSSFP trajectory can display long lengths of the carotid arteries with 1 mm(3) isotropic resolution. J. Magn. Reson. Imaging 2015;41:1150-1156. © 2014 Wiley Periodicals, Inc.

A variational method for the calculation of spin-rovibronic energy levels of any triatomic molecule in an electronic triplet state

The triatomic spin-rovibronic variational code RVIB3 has been extended to include the effect of two uncoupled electrons, for both (3)Sigma(-) and (3)Pi (Renner-Teller) electronic states. The spin-orbital-rotational kinetic energy is included in the usual way, via terms (J+L+S). The phenomenological terms AL.S and lambda 2/3(3S(z)(2)) are introduced to reproduce the 3 spin-orbit and spin-spin splittings, respectively. Calculations are performed to evaluate the spin-rovibronic energy levels of CCO (X) over tilde (3) Sigma(-) and CCO (A) over tilde (3) Pi for which the Born-Oppenheimer potentials are derived from high-accuracy ab initio calculations.

Search for a narrow, spin-2 resonance decaying to a pair of Z bosons in the qq̄ℓ+ℓ- final state

Results are presented from a search for a narrow, spin-2 resonance decaying into a pair of Z bosons, with one Z-boson decaying into leptons (e+e- or μ+μ-) and the other into jets. An example of such a resonance is the Kaluza-Klein graviton, GKK, predicted in Randall-Sundrum models. The analysis is based on a 4.9 fb-1 sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected with the CMS detector at the LHC. Kinematic and topological properties including decay angular distributions are used to discriminate between signal and background. No evidence for a resonance is observed, and upper limits on the production cross sections times branching fractions are set. In two models that predict Z-boson spin correlations in graviton decays, graviton masses are excluded lower than a value which varies between 610 and 945 GeV, depending on the model and the strength of the graviton couplings. © 2012 CERN.

Conservation laws for Z(N) symmetric quantum spin models and their exact ground state energies

We derive an infinite set of conserved charges for some Z(N) symmetric quantum spin models by constructing their Lax pairs. These models correspond to the Potts model, Ashkin-Teller model and the particular set of self-dual Z(N) models solved by Fateev and Zamolodchikov [6]. The exact ground state energy for this last family of hamiltonians is also presented. © 1986.

The Ground State Energy per Site of the Quantum and Classical Edwards-Anderson Spin Glass in the Thermodynamic Limit

We derive general rigorous lower bounds for the average ground state energy per site e ((d)) of the quantum and classical Edwards-Anderson spin-glass model in dimensions d=2 and d=3 in the thermodynamic limit. For the classical model they imply that e ((2))a parts per thousand yena'3/2 and e ((3))a parts per thousand yena'2.204a <-.

Quantum Energy Teleportation Between Spin Particles in a Gibbs State

Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance-quantum correlation in separable states-is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.

Advanced morphological 3D magnetic resonance observation of cartilage repair tissue (MOCART) scoring using a new isotropic 3D proton-density, turbo spin echo sequence with variable flip angle distribution (PD-SPACE) compared to an isotropic 3D steady-state free precession sequence (True-FISP) and standard 2D sequences

To evaluate a new isotropic 3D proton-density, turbo-spin-echo sequence with variable flip-angle distribution (PD-SPACE) sequence compared to an isotropic 3D true-fast-imaging with steady-state-precession (True-FISP) sequence and 2D standard MR sequences with regard to the new 3D magnetic resonance observation of cartilage repair tissue (MOCART) score.