Parametric finite-element studies on the effect of tool shape in friction stir welding

The success of the Friction Stir Welding (FSW) process, and the weld quality produced, depends significantly on the design of the welding tool. In this paper the effect of variation in various tool geometry parameters on FSW process outcomes, during the plunge stage, were investigated. Specifically the tool shoulder surface angle and the ratio of the shoulder radius to pin radius on tool reaction force, tool torque, heat generation, temperature distribution and size of the weld zone were investigated. The studies were carried out numerically using the finite element method. The welding process used AA2024 aluminium alloy plates with a thickness of 3 mm. It was found that, in plunge stage, the larger the pin radius the higher force and torque the tool experiences and the greater heat generated. It is also found that the shoulder angle has very little effect on energy dissipation as well as little effect on temperature distribution

Absence of superconductivity in the half-filled band Hubbard model on the anisotropic triangular lattice

We report exact calculations of magnetic and superconducting pair-pair correlations for the half-filled band Hubbard model on an anisotropic triangular lattice. Our results for the magnetic phases are similar to those obtained with other techniques. The superconducting pair-pair correlations at distances beyond nearest neighbor decrease monotonically with increasing Hubbard interaction U for all anisotropy, indicating the absence of frustration-driven superconductivity within the model.Comment: 4 pages, 4 EPS figure

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

Large-ss expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number ss

The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-$s$ Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattie magnetization), the spin stiffness and the zero-field (uniform, transverse) magnetic susceptibility, for all values of the spin quantum number $s$ in the range $\frac{1}{2} \leq s \leq \frac{9}{2}$. The CCM data points are used to calculate the leading quantum corrections to the classical ($s \rightarrow \infty$) values of these low-energy parameters, considered as large-$s$ asymptotic expansions