Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This makes it difficult to study low-temperature physics of these frustrated systems by using Monte Carlo simulation with the standard single-spin flip algorithm. A typical example is the so-called spin ice model, frustrated ferromagnets on the pyrochlore lattice. The difficulty can be avoided by a global-flip algorithm, the loop algorithm, that enables to sample over the entire discrete manifold and to investigate low-temperature properties. We extend the loop algorithm to Heisenberg spin systems with strong easy-axis anisotropy in which the ground-state manifold is continuous but still retains the spin-ice type degeneracy. We examine different ways of loop flips and compare their efficiency. The extended loop algorithm is applied to the following two models, a Heisenberg antiferromagnet with easy-axis anisotropy along the z axis, and a Heisenberg spin ice model with the local easy-axis anisotropy. For both models, we demonstrate high efficiency of our loop algorithm by revealing the low-temperature properties which were hard to access by the standard single-spin flip algorithm. For the former model, we examine the possibility of order-from-disorder and critically check its absence. For the latter model, we elucidate a gas-liquid-solid transition, namely, crossover or phase transition among paramagnet, spin-ice liquid, and ferromagnetically-ordered ice-rule state.Comment: 12 pages, 11 figures, accepted for publication in Phys. Rev.

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Quantum Monte Carlo study of the transverse-field Ising model on a frustrated checkerboard lattice

We present the numerical results for low temperature behavior of the transverse-field Ising model on a frustrated checkerboard lattice, with focus on the effect of both quantum and thermal fluctuations. Applying the recently-developed continuous-time quantum Monte Carlo algorithm, we compute the magnetization and susceptibility down to extremely low temperatures while changing the magnitude of both transverse and longitudinal magnetic fields. Several characteristic behaviors are observed, which were not inferred from the previously studied quantum order from disorder at zero temperature, such as a horizontal-type stripe ordering at a substantial longitudinal field and a persistent critical behavior down to low temperature in a weak longitudinal field region.Comment: 6 pages, 5 figures, accepted for publication in J. Phys.: Conf. Se

Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Bauordnung für das Königreich Württemberg vom 28. Juli 1910

BAUORDNUNG FÜR DAS KÖNIGREICH WÜRTTEMBERG VOM 28. JULI 1910 Bauordnung für das Königreich Württemberg vom 28. Juli 1910 (-) Einband (-) Titelseite (-) Vorwort (-) Inhaltsverzeichnis (-) Erklärung der Abkürzungen (-) Bauberechtigung und Bauvorschriften im allgemeinen ([1]) Anlage der Orte und Ortstraßen (5) Polizeiliche Bestimmungen für die einzelnen Bauten (29) Allgemeine Bestimmungen (29) Stellung und Lage der Bauten und ihr Verhältnis zu den Straßen und benachbarten Gebäuden und Grundstücken (32) Ausführung der Bauten (65) Baulastenbuch (89) Zuständigkeit der Behörden, Verfahren und Kosten in Bausachen (92) Schlussbestimmungen (117) Alphabetisches Sachregister (120) Farbinformation (-) Einband (-

Combined Analysis of X-Ray Spectra of NGC 3227

The 1.5 Seyfert galaxy NGC 3227 has been observed by several X-ray missions. We carried out combined analysis of the data obtained by more recent major observations of this source - two observations performed by XMM-Newton in 2000 and 2006 and six observations performed by Suzaku in 2008. A unified model was constructed which is consistent with all eight of the observations by the two satillites with large intensity and spectral changes. The model consists of a hard power law with the spectral index of Gamma_Hard=1.4-1.7 which is interpreted as the Comptonized emission from the corona above an accretion disk. In the high flux states an additional soft excess component dominates, which is consistent with a model with either a steeper power law with Gamma_Soft=3.3-3.85 or the warm Comptonization component. These emissions from the central engine are absorbed by a neutral partial covering material and warm absorbers. A reflection component and several emission lines are also present. We examined the relationship between the intrinsic luminosity and the absorbers' physical parameters such as the column density, which suggests that the source expanded significantly during the bright states where the soft excess is greatly enhanced.Comment: 24 pages, 5 tables, and 17 figure

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure