The B\to D_s^{(*)}\eta^{(\prime)} decays in the perturbative QCD

In this paper, we calculate the branching ratios for $B^+\to D_s^+\eta, B^+\to D_s^+\eta^{\prime}$, $B^+\to D_s^{*+}\eta$ and $B^+\to D_s^{*+}\eta^{\prime}$ decays by employing the perturbative QCD (pQCD) factorization approach. Under the two kinds of $\eta-\eta^{\prime}$ mixing schemes, the quark-flavor mixing scheme and the singlet-octet mixing scheme, we find that the calculated branching ratios are consistent with the currently available experimental upper limits. We also considered the so called "$f_{D_s}$ puzzle", by using two groups of parameters about the $D^{(*)}_s$ meson decay constants, that is $f_{D_s}=241$ MeV, $f_{D^*_s}=272$ MeV and $f_{D_s}=274$ MeV, $f_{D^*_s}=312$ MeV, to calculate the branching ratios for the considered decays. We find that the results change $30\%$ by using these two different groups of paramters.Comment: 12 pages, 1 figure. Typos removed, minor correction

Magneto-Centrifugal Launching of Jets from Accretion Disks. I: Cold Axisymmetric Flows

The magneto-centrifugal model for jet formation is studied by time-dependent simulations reaching steady state in a cold gas with negligible fluid pressure, in an axisymmetric geometry, using a modification of the Zeus3D code adapted to parallel computers. The number of boundary conditions imposed at the coronal base takes into account the existence of the fast and Alfvenic critical surfaces, avoiding over-determination of the flow. The size and shape of the computational box is chosen to include these critical surfaces, reducing the influence of the outer boundary conditions. As there is a region, near the origin, where the inclination of field lines to the axis is too small to drive a centrifugal wind, we inject a thin, axial jet, expected to form electromagnetically near black holes. Acceleration and collimation appear for wide generic conditions. A reference run is shown in detail, with a wind leaving the computational volume in the axial direction with a poloidal velocity equal to 4 times the poloidal Alfven speed, collimated inside 11 degrees. Finally, the critical surfaces, fieldlines, thrust, energy, torque and mass discharge of the outgoing wind are shown for simulations with various profiles of mass and magnetic flux at the base of the corona.Comment: 27 pages, including 10 figures and 2 tables. To appear in ApJ (Dec 1999). Revised version clarifies the abstract, section 3.2.4, conclusions and appendix, adds a simulation to section 4.2, and updates the reference

The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUBmm Approximation Scheme for Lattice Models

A new approximation hierarchy, called the LPSUB$m$ scheme, is described for the coupled cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-1/2 Heisenberg antiferromagnetic) spin-lattice models, namely: the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods and the CCM using the alternative LSUB$m$ and DSUB$m$ schemes. Each of the three CCM schemes (LSUB$m$, DSUB$m$ and LPSUB$m$) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications

Transverse Magnetic Susceptibility of a Frustrated Spin-12\frac{1}{2} J1J_{1}--J2J_{2}--J1⊥J_{1}^{\perp} Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice

We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv \delta J_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field transverse magnetic susceptibility $\chi$ in the N\'eel phase. We thus obtain an accurate estimate of the full boundary of the N\'eel phase in the $\kappa\delta$ plane for the zero-temperature quantum phase diagram. We demonstrate explicitly that the phase boundary derived from $\chi$ is fully consistent with that obtained from the vanishing of the N\'eel magnetic order parameter. We thus conclude that at all points along the N\'eel phase boundary quasiclassical magnetic order gives way to a nonclassical paramagnetic phase with a nonzero energy gap. The N\'eel phase boundary exhibits a marked reentrant behavior, which we discuss in detail

Collinear antiferromagnetic phases of a frustrated spin-12\frac{1}{2} J1J_{1}--J2J_{2}--J1⊥J_{1}^{\perp} Heisenberg model on an AAAA-stacked bilayer honeycomb lattice

The zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} \equiv \kappa J_{1}>0$. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_{1}^{\perp} \equiv \delta J_{1}$. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the N\'{e}el and N\'{e}el-II phases, are calculated in the $\kappa \delta$ half-plane with $\kappa > 0$. Whereas on each monolayer in the N\'{e}el state all NN pairs of spins are antiparallel, in the N\'{e}el-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter $M$ and the excitation energy $\Delta$ from the $s^{z}_{T}=0$ ground state to the lowest-lying $|s^{z}_{T}|=1$ excited state (where $s^{z}_{T}$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders ($n \leq 10$) in a systematic series of approximations involving $n$-spin clusters. The sole approximation made is then to extrapolate the sequences of $n$th-order results for $M$ and $\Delta$ to the exact limit, $n \to \infty$

A high-order study of the quantum critical behavior of a frustrated spin-12\frac{1}{2} antiferromagnet on a stacked honeycomb bilayer

We study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on an $AA$-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings $J_{1}$, $J_{2}$, and $J_{3}$, respectively. The two layers are coupled with an AFM NN exchange coupling $J_{1}^{\perp}\equiv\delta J_{1}$. The model is studied for arbitrary values of $\delta$ along the line $J_{3}=J_{2}\equiv\alpha J_{1}$ that includes the most highly frustrated point at $\alpha=\frac{1}{2}$, where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the $\alpha\delta$ plane in the window $0 \leq \alpha \leq 1$, $0 \leq \delta \leq 1$. This includes two AFM phases with N\'eel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, $\delta = \delta_{c_{i}}(\alpha)$, or equivalently, $\alpha = \alpha_{c_{i}}(\delta)$, with $i=1$ (N\'eel) and 2 (striped). The two boundaries exhibit an "avoided crossing" behavior with both curves being reentrant

Ground-state phases of the spin-1 J1J_{1}--J2J_{2} Heisenberg antiferromagnet on the honeycomb lattice

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv \kappa J_{1} > 0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0 < \kappa < 1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el order for $\kappa < \kappa_{c_{1}} = 0.250(5)$, and another with 4-sublattice N\'{e}el-II order for $\kappa > \kappa_{c_{2}} = 0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range $\kappa_{c_{1}} < \kappa < \kappa^{i}_{c} = 0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range $\kappa^{i}_{c} < \kappa < \kappa_{c_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry