Lattice Units Research Articles

Effective Polyakov line action from strong lattice couplings to the deconfinement transition

We calculate the effective Polyakov line action corresponding to SU(2) lattice gauge theory on a 16^3 X 4 lattice via the "relative weights" method. We consider a variety of lattice couplings, ranging from beta=1.2 in the strong-coupling domain, to beta=2.3 at the deconfinement transition, in order to study how the effective action evolves with beta. Comparison of Polyakov line correlators computed in the effective theory and the underlying gauge theory is used to test the validity of the effective action for beta > 1.4, while for beta=1.2, 1.4 we can compare our effective action to the one obtained from a low-order strong-coupling expansion. Very good agreement is found at all couplings. We find that the effective action is given by a simple expression bilinear in the Polyakov lines. The range of the bilinear term, away from strong coupling, grows rapidly in lattice units as beta increases.

Magnetic ordering in GdNi2B2C revisited by resonant x-ray scattering: Evidence for the double-qmodel

Recent theoretical efforts aimed at understanding the nature of antiferromagnetic ordering in GdNi${}_{2}$B${}_{2}$C predicted double-$q$ ordering. Here we employ resonant elastic x-ray scattering to test this theory against the formerly proposed, single-$q$ ordering scenario. Our study reveals a satellite reflection associated with a mixed-order component propagation wave vector, viz., (${q}_{a},2{q}_{b},0$) with ${q}_{b}={q}_{a}\ensuremath{\approx}0.55$ reciprocal lattice units, the presence of which is incompatible with single-$q$ ordering but is expected from the double-$q$ model. A ($3{q}_{a},0,0$) wave vector (i.e., third-order) satellite is also observed, again in line with the double-$q$ model. The temperature dependencies of these along with that of a first-order satellite are compared with calculations based on the double-$q$ model and reasonable qualitative agreement is found. By examining the azimuthal dependence of first-order satellite scattering, we show the magnetic order to be, as predicted, elliptically polarized at base temperature and find the temperature dependence of the ``out of $a$-$b$ plane'' moment component to be in fairly good agreement with calculation. Our results provide qualitative support for the double-$q$ model and thus in turn corroborate the explanation for the ``magnetoelastic paradox'' offered by this model.

QCD with two light dynamical chirally improved quarks: Baryons

We present a study of baryon ground states and low lying excitations of nonstrange and strange baryons. The results are based on seven gauge field ensembles with two dynamical light chirally improved quarks corresponding to pion masses between 255 and 596 MeV and a strange valence quark with mass fixed by the $\ensuremath{\Omega}$ baryon. The lattice spacing varies between 0.1324 and 0.1398 fm. Given in lattice units, the bulk of our results are for size ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$; for two ensembles with light pion masses (255 and 330 MeV) we also use ${24}^{3}\ifmmode\times\else\texttimes\fi{}48$ lattices and perform an infinite volume extrapolation. We derive energy levels for the spin $1/2$ and $3/2$ channels for both parities. In general, our results in the infinite volume limit compare well with experiment. We analyze the flavor symmetry content by identifying the singlet/octet/decuplet contributions of the resulting eigenstates. The ground states' compositions agree with quark model expectations. In some cases the excited states, however, disagree and we discuss possible reasons.

Transfer matrix for Kogut-Susskind fermions in the spin basis

In the absence of interaction, it is well known that the Kogut-Susskind regularizations of fermions in the spin and flavor basis are equivalent to each other. In this paper, we clarify the difference between the two formulations in the presence of interaction with gauge fields. We then derive an explicit expression of the transfer matrix in the spin basis by a unitary transformation on that one in the flavor basis which is known. The essential key ingredient is the explicit construction of the fermion Fock space for variables which live on blocks. Therefore, the transfer matrix generates time translations of two lattice units.

Bayesian spatial-temporal autologistic regression model on dengue hemorrhagic fever in east Java, Indonesia

The purpose of this study is to discuss and develop Spatial- Temporal Autologistic Regression Model (STARM) to represent spreading of the Aedes aegypti which is indicated by the endemic level of DHF (Dengue Hemorrhagic Fever) in East Java. The method which is used to estimate STARM parameter is Bayesian method with Markov Chain Monte Carlo (MCMC) and Gibbs Sampler simulation. This study observed 38 districts as spatial lattice units, meanwhile temporal unit is represented by monthly period of evidence (January-December) in 2002-2008. Result of the research was obtained STARM model that indicate the spreading pattern of the Aedes aegypti that is indicated by the endemic level of DHF incidence in East Java have spatially and temporally positive correlation. Model validation using 95% credible interval shows that all estimators are significant. This is also supported by a MAE value 0.09 and the percentage of correctly classified predicted data 90%, which means there are 90 correctly classified data of 100 prediction data.

ChemInform Abstract: Long‐Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x.

AbstractResonant soft X‐ray scattering is used to identify two‐dimensional charge fluctuations with an incommensurate periodicity of about 3.2 lattice units in the copper oxide planes of the title superconductors.

Two-dimensional distributed-feedback in InGaAs/GaAs quantum structure lattice arrays

The spontaneous emission properties of an artificial semiconductor lattice—quantum structure lattice (QSL)—with in-plane two-dimensional distributed-feedback (DFB) are reported. Quantum box arrays fabricated in strained InGaAs/GaAs quantum wells are used as lattice units in the QSL. The photoluminescence (PL) peak wavelength of the QSL shows the characteristic weak temperature dependence of a DFB structure (0.024 nm/K) between 77 and 150 K. The surface emission of the QSL array shows a collimated radiation pattern. The peak PL intensity has maximum values centered within ±30° of the surface normal and dropped off beyond that angle rapidly.

Adsorption of Solvent Cations on Au(111) and Au(100) in Alkylimidazolium-Based Ionic Liquids – Worm-Like versus Micelle-Like Structures

Abstract By employing high resolution in-situ STM, the adsorption of alkylimidazolium-based cations of EMI + , PMI + , BMI + and OMI + on Au(111) and Au(100) surfaces are investigated systematically. The cation adsorption on both Au(111) and Au(100) are composed of double rows arising from counter-facing imidazolium-based cation pairs. On Au(100), the double rows associated with the four cations show micelle-like appearance along the two √ 2 directions of the Au(100) surface lattice units. The width of the double rows varies depending on the side chain length of the cations, but is constrained by the periodicity along the √ 2 directions. Anions of BF 4 - , PF 6 - , CF3SO 3 - and Tf2N - do not influence the micelle-like adsorption structure. On Au(111), the double rows are formed only when the terraces are etched to several atoms wide. Most likely, the underneath Au surface experiences restructuring to accommodate the double row structure, and the worm-like orientation of the double rows is the consequence of strain release. Both the micelle-like and worm-like adsorption structures would be lifted upon cathodic potential excursions when the surfaces are driven to undergo ordinary Au(100)-hex and Au(111)-(√ 3 × 22) reconstructions. These results reveal that the ordered micelle-like structure on Au(100) and the irregular worm-like structure on Au(111) are of the same nature.

Two-color QCD with staggered fermions at finite temperature under the influence of a magnetic field

In this paper we investigate the influence of a constant external magnetic field on the finite-temperature phase structure and the chiral properties of a simplified lattice model for QCD. We assume an $SU(2)$ gauge symmetry and employ dynamical staggered fermions of identical mass without rooting, corresponding to ${N}_{f}=4$ flavors of identical electric charge. For fixed mass (given in lattice units) the critical temperature is seen to rise with the magnetic field strength. For three fixed $\ensuremath{\beta}$ values, selected such that we stay (i) within the chirally broken phase, (ii) within the transition region, or (iii) within the chirally restored phase, we study the approach to the chiral limit for various values of the magnetic field. Within the chirally broken (confinement) phase the chiral condensate is found to increase monotonically with a growing magnetic field strength. In the chiral limit the increase starts linear in agreement with a chiral model studied by Shushpanov and Smilga. Within the chirally restored (deconfinement) phase the chiral condensate tends to zero in the chiral limit, irrespective of the strength of the magnetic field.

Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links

We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain distance r from the corresponding node in network A and vice versa. Our results suggest that percolation for small r below r(max)≈8 (lattice units) is a second-order transition, and for larger r is a first-order transition. For r<r(max), the critical threshold increases linearly with r from 0.593 at r=0 and reaches a maximum, 0.738 for r=r(max), and then gradually decreases to 0.683 for r=∞. Our analytical considerations are in good agreement with simulations. Our study suggests that interdependent infrastructures embedded in Euclidean space become most vulnerable when the distance between interdependent nodes is in the intermediate range, which is much smaller than the size of the system.

Lattice QCD computation of the SU(3) string tension critical curve

We investigate the critical curve of the string tension $\ensuremath{\sigma}(T)$ as a function of temperature in quenched gauge invariant SU(3) lattice gauge theory. We extract $\ensuremath{\sigma}(T)$ from the color averaged free energy of a static quark-antiquark pair. To compute the free energy, we utilize a pair of gauge invariant Polyakov loop and antiloop correlations and apply the multihit procedure to enhance the signal-to-noise ratio. We find that the string tension departs from the zero temperature ${\ensuremath{\sigma}}_{0}$ at $T\ensuremath{\simeq}0.5{T}_{c}$. We cover the relevant temperature range from $0.5{T}_{c}$ up to the confinement temperature ${T}_{c}$ using 54 different sets of pure gauge lattice configurations with four temporal extensions (4, 6, 8, 12), different $\ensuremath{\beta}$, and a spatial volume of ${48}^{3}$ in lattice units.

Common origin of the two types of magnetic fluctuations in iron chalcogenides

We use inelastic neutron scattering to study the low energy spin excitations in moderately doped non-superconducting Fe$_{1.01}$Te$_{0.72}$Se$_{0.28}$. The spin excitations in this system contain components near (0.5,0,0) and (0.5,0.5,0) in a-b plane reciprocal lattice units using tetragonal unit cell notation (a=b=3.772 \AA and c=6.061 \AA). At low energies the scattering is centered around (0.5,0,0). With increasing energy, the spectral weight of low energy spin excitations centered around (0.5,0,0) abruptly shifts around 3 meV to the incommensurate spin excitations centered around (0.5,0.5,0). However both types of spin fluctuations exhibit the identical temperature dependence. These results indicate that the (0.5,0,0) type spin excitations and the incommensurate excitations around the (0.5,0.5,0) position have a common origin and both must be taken into account to understand the nature of magnetism and superconducting pairing in the iron chalcogenides.

Control of spontaneous emission in InGaAs/GaAs quantum structure lattices

We report the control of spontaneous emission wavelength of quantum wells (QWs) using an artificial design of semiconductor lattice, i.e., quantum structure lattice (QSL). Two-dimension square quantum box arrays fabricated in strained InGaAs/GaAs QW samples are used as active lattice units in QSL for this study. The photoluminescence peak wavelength of the QSL can be adjusted to blue-shift, red-shift, or unchanged from that of the as-grown QW by fitting the in-plane Bragg diffraction condition of the QSL. The wavelength-shift has values of multiple phonon energies indicating that the phonon-assisted recombination process may play a significant role in the observed spontaneous emission.

Polarized IR Spectra of the Hydrogen Bond in Two Different Oxindole Polymorphs with Cyclic Dimers in Their Lattices

This article focuses on the problem of remarkably strong changes in the fine structure patterns of the ν(N-H) and ν(N-D) bands attributed to the hydrogen and deuterium bonds accompanying the phase transition, which occurs between two polymorphic forms of oxindole. The lattices of these two different crystals contain hydrogen-bonded cyclic dimers differ in their geometry parameters. The source of these differences in the polymorph spectral properties results from the geometry relations concerning the dimers constituting the lattice structural units. In the case of the "alpha" phase, the hydrogen bond lengths of the dimers differ by 0.18 Å. This leads to the "off-resonance exciton coupling" weakly involving the dimer hydrogen bonds. For the "beta" phase, with practically symmetric dimers in the lattice, the spectra become typical for centrosymmetric hydrogen bond systems due to the full resonance of the proton or deuteron vibrations.

Thermodynamics of lattice QCD with 2 sextet quarks onNt=8lattices

We continue our lattice simulations of QCD with 2 flavors of color-sextet quarks as a model for conformal or walking technicolor. A 2-loop perturbative calculation of the $\ensuremath{\beta}$ function which describes the evolution of this theory's running coupling constant predicts that it has a second zero at a finite coupling. This nontrivial zero would be an infrared stable fixed point, in which case the theory with massless quarks would be a conformal field theory. However, if the interaction between quarks and antiquarks becomes strong enough that a chiral condensate forms before this IR fixed point is reached, the theory is QCD-like with spontaneously broken chiral symmetry and confinement. However, the presence of the nearby IR fixed point means that there is a range of couplings for which the running coupling evolves very slowly, i.e. it ``walks.'' We are simulating the lattice version of this theory with staggered quarks at finite temperature, studying the changes in couplings at the deconfinement and chiral-symmetry restoring transitions as the temporal extent (${N}_{t}$) of the lattice, measured in lattice units, is increased. Our earlier results on lattices with ${N}_{t}=4$, 6 show both transitions move to weaker couplings as ${N}_{t}$ increases consistent with walking behavior. In this paper we extend these calculations to ${N}_{t}=8$. Although both transitions again move to weaker couplings, the change in the coupling at the chiral transition from ${N}_{t}=6$ to ${N}_{t}=8$ is appreciably smaller than that from ${N}_{t}=4$ to ${N}_{t}=6$. This indicates that at ${N}_{t}=4$, 6 we are seeing strong-coupling effects and that we will need results from ${N}_{t}&gt;8$ to determine if the chiral-transition coupling approaches zero as ${N}_{t}\ensuremath{\rightarrow}\ensuremath{\infty}$, as needed for the theory to walk.

Solid‐State Redox Solutions: Microfabrication and Electrochemistry

On solid ground: Mix-valent iron hexacyanides (FeIII, FeII, and Prussian blue) can replace NaCl crystal lattice units to form a solid-state solution. A scanning electrochemical microcapillary (SECM) technique has been developed for the controllable microfabrication of the microcrystals. In situ confocal Raman spectra can also be obtained without exposure to any liquid environment. WE=working electrode, RE/CE=reference/counter electrode.

Azimuthal reflection high-energy electron diffraction study of MnAs growth on GaAs(001) by molecular beam epitaxy

Azimuthal reflection high-energy electron diffraction (ARHEED) and in situ grazing incidence synchrotron x-ray diffraction techniques are employed to investigate the growth, epitaxial orientation, and interfacial structure of MnAs layers grown on GaAs(001) by molecular beam epitaxy (MBE). We demonstrate the power and reliability of ARHEED scans as a routine tool in characterizing the formation of epitaxial films. The ARHEED scans clearly reveal the formation of the rectangular MnAs unit cell during growth on GaAs(001) for a MnAs layer thickness of 2.1 ± 0.2 monolayers with a tensile strain along the MnAs[112−0] direction. A periodic coincidence site lattice, which is known to form along the MnAs [0001] direction to release the strain due to the huge lattice mismatch (∼30%) also produces periodic satellites of the diffraction spots in the ARHEED scan. The formation of different epitaxial orientations of MnAs during MBE growth can be directly observed using ARHEED scans. ARHEED is demonstrated to have a resolution similar to synchrotron x-ray diffraction with a double crystal monochromator, yielding full width at half maximum values of reflections as small as 0.005 reciprocal lattice units.

Molecular dynamics simulation of deposition of nickel nanocluster on copper surface

The burrowing of nickel nanocluster deposited onto the copper surface is investigated by molecular dynamics (MD) simulation. The simulation is carried out at different temperatures for 40.1 ns with three different lattice orientations Cu(100), Cu(110), and Cu(111) that have 20 × 20 × 15, 14 × 14 × 15, and 12 × 14 × 9 lattice units, respectively. The Ni(100) nanocluster consists of 249 atoms (five lattices diameter) and the initial kinetic energy is assigned to be 0 eV. The results show that the burrowing process goes extremely slow as temperature is at or under 900 K. There is virtually no burrowing observed when the system temperature is below 500 K. The burrowing processes at different temperatures are discussed in terms of kinetic energy of the cluster exerted by the strong capillary force. It is found that the kinetic energy will play a key role in the acceleration of the burrowing process.

Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

This study presents the integration of isotropic color gradient discretization into a lattice Boltzmann Rothman–Keller (RK) model designed for two-phase flow simulation. The proposed model removes one limitation of the RK model, which concerns the handling of O(1000) large density ratios between the fluids for a wide range of parameters. Taylor’s series expansions are used to characterize the difference between an isotropic gradient discretization and the commonly used anisotropic gradient. The proposed color gradient discretization can reduce, by one order of magnitude, the spurious current problem that affects the interface between the phases. A set of numerical tests is conducted to show that a rotationally invariant discretization enables widening of the parameter range for the surface tension. Surface tensions from O(10 −2) to O(10 −8), depending on the density ratio, are accurately simulated. An extreme density ratio of O(10,000) is successfully tested for a steady bubble with an error of 0.5% for Laplace’s law across a sharp interface, with a thickness of about 5–6 lattice units.

Broken Even-Odd Symmetry in Self-Selection of Distances between Nanoclusters due to the Presence or Absence of Topological Solitons

Depositing particles randomly on a 1D lattice is expected to result in an equal number of particle pairs separated by even or odd lattice units. Unexpectedly, the even-odd symmetry is broken in the self-selection of distances between indium magic-number clusters on a Si(100)-2×1 reconstructed surface. Cluster pairs separated by even units are less abundant because they are linked by silicon atomic chains carrying topological solitons, which induce local strain and create localized electronic states with higher energy. Our findings reveal a unique particle-particle interaction mediated by the presence or absence of topological solitons on alternate lattices.