19,484 research outputs found
Simple-Current Symmetries, Rank-Level Duality, and Linear Skein Relations for Chern-Simons Graphs
A previously proposed two-step algorithm for calculating the expectation
values of Chern-Simons graphs fails to determine certain crucial signs. The
step which involves calculating tetrahedra by solving certain non- linear
equations is repaired by introducing additional linear equations. As a first
step towards a new algorithm for general graphs we find useful linear equations
for those special graphs which support knots and links. Using the improved set
of equations for tetrahedra we examine the symmetries between tetrahedra
generated by arbitrary simple currents. Along the way we uncover the classical
origin of simple-current charges. The improved skein relations also lead to
exact identities between planar tetrahedra in level and level
CS theories, where denotes a classical group. These results are
recast as identities for quantum -symbols and WZW braid matrices. We obtain
the transformation properties of arbitrary graphs and links under simple
current symmetries and rank-level duality. For links with knotted components
this requires precise control of the braid eigenvalue permutation signs, which
we obtain from plethysm and an explicit expression for the (multiplicity free)
signs, valid for all compact gauge groups and all fusion products.Comment: 58 pages, BRX-TH-30
Investigation of the oxohalogenide Cu4Te5O12Cl4 with weakly coupled Cu(II) tetrahedra
The crystal structure of the copper(II) tellurium(IV) oxochloride
CuTeOCl (Cu-45124) is composed of weakly coupled
tetrahedral Cu clusters and shows crystallographic similarities with the
intensively investigated compound CuTeOX, with X~=~Cl,
Br (Cu-2252). It differs from the latter by a larger separation of the
tetrahedra within the crystallographic ab plane, that allows a more direct
assignment of important inter-tetrahedra exchange paths and the existence of an
inversion center. Magnetic susceptibility and specific heat evidence
antiferromagnetic, frustrated correlations of the Cu spin moments and long
range ordering with =13.6 K. The entropy related to the transition is
reduced due to quantum fluctuations. In Raman scattering a well structured low
energy magnetic excitation is observed at energies of 50K
(35cm. This energy scale is reduced as compared to Cu-2252.Comment: 11 pages, 9 figures, further information see
http://www.peter-lemmens.d
Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
Systems of hard nonspherical particles exhibit a variety of stable phases
with different degrees of translational and orientational order, including
isotropic liquid, solid crystal, rotator and a variety of liquid crystal
phases. In this paper, we employ a Monte Carlo implementation of the
adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to
ascertain with high precision the equilibrium phase behavior of systems of
congruent Archimedean truncated tetrahedra over the entire range of possible
densities up to the maximal nearly space-filling density. In particular, we
find that the system undergoes two first-order phase transitions as the density
increases: first a liquid-solid transition and then a solid-solid transition.
The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase
at intermediate densities. At higher densities, we find that the CT phase
undergoes another first-order phase transition to one associated with the
densest-known crystal. We find no evidence for stable rotator (or plastic) or
nematic phases. We also generate the maximally random jammed (MRJ) packings of
truncated tetrahedra, which may be regarded to be the glassy end state of a
rapid compression of the liquid. We find that such MRJ packings are
hyperuniform with an average packing fraction of 0.770, which is considerably
larger than the corresponding value for identical spheres (about 0.64). We
conclude with some simple observations concerning what types of phase
transitions might be expected in general hard-particle systems based on the
particle shape and which would be good glass formers
On canonical triangulations of once-punctured torus bundles and two-bridge link complements
We prove the hyperbolization theorem for punctured torus bundles and
two-bridge link complements by decomposing them into ideal tetrahedra which are
then given hyperbolic structures, following Rivin's volume maximization
principle.Comment: This is the version published by Geometry & Topology on 16 September
2006. Appendix by David Fute
Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity
In this paper we are interested in computing representations of the
fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C);
PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated
tetrahedra of flags. We list complete computations (giving 0-dimensional or
1-dimensional solution sets) for the first complete hyperbolic non-compact
manifolds with finite volume which are obtained gluing less than three
tetrahedra with a description of the computer methods used to find them
Thermodynamic Bethe Ansatz and Threefold Triangulations
In the Thermodynamic Bethe Ansatz approach to 2D integrable, ADE-related
quantum field theories one derives a set of algebraic functional equations (a
Y-system) which play a prominent role. This set of equations is mapped into the
problem of finding finite triangulations of certain 3D manifolds. This mapping
allows us to find a general explanation of the periodicity of the Y-system. For
the related theories and more generally for the various restrictions of
the fractionally-supersymmetric sine-Gordon models, we find an explicit,
surprisingly simple solution of such functional equations in terms of a single
unknown function of the rapidity. The recently-found dilogarithm functional
equations associated to the Y-system simply express the invariance of the
volume of a manifold for deformations of its triangulations.Comment: 17 pages, 2 eps figures, enlarged version to appear in IJMP
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