5,129 research outputs found
How Do Quasicrystals Grow?
Using molecular simulations, we show that the aperiodic growth of
quasicrystals is controlled by the ability of the growing quasicrystal
`nucleus' to incorporate kinetically trapped atoms into the solid phase with
minimal rearrangement. In the system under investigation, which forms a
dodecagonal quasicrystal, we show that this process occurs through the
assimilation of stable icosahedral clusters by the growing quasicrystal. Our
results demonstrate how local atomic interactions give rise to the long-range
aperiodicity of quasicrystals.Comment: 4 pages, 4 figures. Figures and text have been updated to the final
version of the articl
Dilute Birman--Wenzl--Murakami Algebra and models
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is
considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra.
The vertex models are examples of corresponding solvable
lattice models and can be regarded as the dilute version of the
vertex models.Comment: 11 page
Non-universal behavior for aperiodic interactions within a mean-field approximation
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit,
with the interaction constants following two deterministic aperiodic sequences:
Fibonacci or period-doubling ones. New algorithms of sequence generation were
implemented, which were fundamental in obtaining long sequences and, therefore,
precise results. We calculate the exact critical temperature for both
sequences, as well as the critical exponent , and . For
the Fibonacci sequence, the exponents are classical, while for the
period-doubling one they depend on the ratio between the two exchange
constants. The usual relations between critical exponents are satisfied, within
error bars, for the period-doubling sequence. Therefore, we show that
mean-field-like procedures may lead to nonclassical critical exponents.Comment: 6 pages, 7 figures, to be published in Phys. Rev.
Quantum Fluctuations and Excitations in Antiferromagnetic Quasicrystals
We study the effects of quantum fluctuations and the excitation spectrum for
the antiferromagnetic Heisenberg model on a two-dimensional quasicrystal, by
numerically solving linear spin-wave theory on finite approximants of the
octagonal tiling. Previous quantum Monte Carlo results for the distribution of
local staggered magnetic moments and the static spin structure factor are
reproduced well within this approximate scheme. Furthermore, the magnetic
excitation spectrum consists of magnon-like low-energy modes, as well as
dispersionless high-energy states of multifractal nature. The dynamical spin
structure factor, accessible to inelastic neutron scattering, exhibits
linear-soft modes at low energies, self-similar structures with bifurcations
emerging at intermediate energies, and flat bands in high-energy regions. We
find that the distribution of local staggered moments stemming from the
inhomogeneity of the quasiperiodic structure leads to a characteristic energy
spread in the local dynamical spin susceptibility, implying distinct nuclear
magnetic resonance spectra, specific for different local environments.Comment: RevTex, 12 pages with 15 figure
Saturation of Cs2 Photoassociation in an Optical Dipole Trap
We present studies of strong coupling in single-photon photoassociation of
cesium dimers using an optical dipole trap. A thermodynamic model of the trap
depletion dynamics is employed to extract absolute rate coefficents. From the
dependence of the rate coefficient on the photoassociation laser intensity, we
observe saturation of the photoassociation scattering probability at the
unitarity limit in quantitative agreement with the theoretical model by Bohn
and Julienne [Phys. Rev. A, 60, 414 (1999)]. Also the corresponding power
broadening of the resonance width is measured. We could not observe an
intensity dependent light shift in contrast to findings for lithium and
rubidium, which is attributed to the absence of a p or d-wave shape resonance
in cesium
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
The bubble algebra: structure of a two-colour Temperley–Lieb Algebra
We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley–Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang–Baxter equations
In search of multipolar order on the Penrose tiling
Based on Monte Carlo calculations, multipolar ordering on the Penrose tiling,
relevant for two-dimensional molecular adsorbates on quasicrystalline surfaces
and for nanomagnetic arrays, has been analyzed. These initial investigations
are restricted to multipolar rotors of rank one through four - described by
spherical harmonics Ylm with l=1...4 and restricted to m=0 - positioned on the
vertices of the rhombic Penrose tiling. At first sight, the ground states of
odd-parity multipoles seem to exhibit long-range multipolar order, indicated by
the appearance of a superstructure in the form of the decagonal
Hexagon-Boat-Star tiling, in agreement with previous investigations of dipolar
systems. Yet careful analysis establishes that long-range multipolar order is
absent in all cases investigated here, and only short-range order exists. This
result should be taken as a warning for any future analysis of order in either
real or simulated arrangements of multipoles on quasiperiodic templates
Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: a renormalization-group approach
Using a real-space renormalization-group approximation, we study the
anisotropic quantum Heisenberg model on hierarchical lattices, with
interactions following aperiodic sequences. Three different sequences are
considered, with relevant and irrelevant fluctuations, according to the
Luck-Harris criterion. The phase diagram is discussed as a function of the
anisotropy parameter (such that and correspond
to the isotropic Heisenberg and Ising models, respectively). We find three
different types of phase diagrams, with general characteristics: the isotropic
Heisenberg plane is always an invariant one (as expected by symmetry arguments)
and the critical behavior of the anisotropic Heisenberg model is governed by
fixed points on the Ising-model plane. Our results for the isotropic Heisenberg
model show that the relevance or irrelevance of aperiodic models, when compared
to their uniform counterpart, is as predicted by the Harris-Luck criterion. A
low-temperature renormalization-group procedure was applied to the
\textit{classical} isotropic Heisenberg model in two-dimensional hierarchical
lattices: the relevance criterion is obtained, again in accordance with the
Harris-Luck criterion.Comment: 6 pages, 3 figures, to be published in Phys. Rev.
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
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