308 research outputs found
Duality and conformal twisted boundaries in the Ising model
There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper symmetry of the model at criticality. Thus, at criticality, the duality-twisted Ising model is translationally invariant, similar to the more familiar cases of periodic and antiperiodic boundary conditions. The complete finite-size spectrum of the Ising quantum chain with this peculiar boundary condition is obtained
Dilute Algebras and Solvable Lattice Models
The definition of a dilute braid-monoid algebra is briefly reviewed. The
construction of solvable vertex and interaction-round-a-face models built on
representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras
is discussed.Comment: 8 pages, uuencoded gz-compressed PostScript, to appear in the
proceedings of the satellite meeting of STATPHYS 19, `Statistical Models,
Yang-Baxter Equation and Related Topics', August 8-10, 1995, Tianjin, Chin
The modified XXZ Heisenberg chain, conformal invariance, surface exponents of c<1 systems, and hidden symmetries of the finite chains
The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is
considered. For the first type, the Hamiltonian is hermitian but not for the
second type which includes the U_{q}[SU(2)] symmetric case. It is shown that
for a certain `tuning' between the anisotropy angle and the boundary terms the
spectra present unexpected degeneracies. These degeneracies are related to the
structure of the irreducible representations of the Virasoro algebras for c<1.Comment: 9 pages; an old preprint from the pre-arXiv (but not pre-LaTeX) era,
published version not (yet?) electronically accessibl
Can Kinematic Diffraction Distinguish Order from Disorder?
Diffraction methods are at the heart of structure determination of solids.
While Bragg-like scattering (pure point diffraction) is a characteristic
feature of crystals and quasicrystals, it is not straightforward to interpret
continuous diffraction intensities, which are generally linked to the presence
of disorder. However, based on simple model systems, we demonstrate that it may
be impossible to draw conclusions on the degree of order in the system from its
diffraction image. In particular, we construct a family of one-dimensional
binary systems which cover the entire entropy range but still share the same
purely diffuse diffraction spectrum.Comment: 5 pages, 1 figure; two typos in the recursion relations for the
autocorrelation coefficients were correcte
Surprises in aperiodic diffraction
Mathematical diffraction theory is concerned with the diffraction image of a
given structure and the corresponding inverse problem of structure
determination. In recent years, the understanding of systems with continuous
and mixed spectra has improved considerably. Moreover, the phenomenon of
homometry shows various unexpected new facets. Here, we report on some of the
recent results in an exemplary and informal fashion.Comment: 9 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool
Combinatorial problems of (quasi-)crystallography
Several combinatorial problems of (quasi-)crystallography are reviewed with
special emphasis on a unified approach, valid for both crystals and
quasicrystals. In particular, we consider planar sublattices, similarity
sublattices, coincidence sublattices, their module counterparts, and central
and averaged shelling. The corresponding counting functions are encapsulated in
Dirichlet series generating functions, with explicit results for the triangular
lattice and the twelvefold symmetric shield tiling. Other combinatorial
properties are briefly summarised.Comment: 12 pages, 2 PostScript figures, LaTeX using vch-book.cl
A Note on Shelling
The radial distribution function is a characteristic geometric quantity of a
point set in Euclidean space that reflects itself in the corresponding
diffraction spectrum and related objects of physical interest. The underlying
combinatorial and algebraic structure is well understood for crystals, but less
so for non-periodic arrangements such as mathematical quasicrystals or model
sets. In this note, we summarise several aspects of central versus averaged
shelling, illustrate the difference with explicit examples, and discuss the
obstacles that emerge with aperiodic order.Comment: substantially revised and extended, 15 pages, AMS LaTeX, several
figures included; see also math.MG/990715
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