11,242 research outputs found
Gas release and conductivity modification studies
The behavior of gas clouds produced by releases from orbital velocity in either a point release or venting mode is described by the modification of snowplow equations valid in an intermediate altitude regime. Quantitative estimates are produced for the time dependence of the radius of the cloud, the average internal energy, the translational velocity, and the distance traveled. The dependence of these quantities on the assumed density profile, the internal energy of the gas, and the ratio of specific heats is examined. The new feature is the inclusion of the effect of the large orbital velocity. The resulting gas cloud models are used to calculate the characteristics of the field line integrated Pedersen conductivity enhancements that would be produced by the release of barium thermite at orbital velocity in either the point release or venting modes as a function of release altitude and chemical payload weight
Some comments on developments in exact solutions in statistical mechanics since 1944
Lars Onsager and Bruria Kaufman calculated the partition function of the
Ising model exactly in 1944 and 1949. Since then there have been many
developments in the exact solution of similar, but usually more complicated,
models. Here I shall mention a few, and show how some of the latest work seems
to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise
The order parameter of the chiral Potts model
An outstanding problem in statistical mechanics is the order parameter of the
chiral Potts model. An elegant conjecture for this was made in 1983. It has
since been successfully tested against series expansions, but as far as the
author is aware there is as yet no proof of the conjecture. Here we show that
if one makes a certain analyticity assumption similar to that used to derive
the free energy, then one can indeed verify the conjecture. The method is based
on the ``broken rapidity line'' approach pioneered by Jimbo, Miwa and
Nakayashiki.Comment: 29 pages, 7 figures. Citations made more explicit and some typos
correcte
Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem
The partition function of the Baxter-Wu model is exactly related to the
generating function of a site-colouring problem on a hexagonal lattice. We
extend the original Bethe ansatz solution of these models in order to obtain
the eigenspectra of their transfer matrices in finite geometries and general
toroidal boundary conditions. The operator content of these models are studied
by solving numerically the Bethe-ansatz equations and by exploring conformal
invariance. Since the eigenspectra are calculated for large lattices, the
corrections to finite-size scaling are also calculated.Comment: 12 pages, latex, to appear in J. Phys. A: Gen. Mat
Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
We prove that the -state Potts antiferromagnet on a lattice of maximum
coordination number exhibits exponential decay of correlations uniformly at
all temperatures (including zero temperature) whenever . We also prove
slightly better bounds for several two-dimensional lattices: square lattice
(exponential decay for ), triangular lattice (), hexagonal
lattice (), and Kagom\'e lattice (). The proofs are based on
the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex
file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 ps file
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
The construction of auxiliary matrices for the six-vertex model at a root of
unity is investigated from a quantum group theoretic point of view. Employing
the concept of intertwiners associated with the quantum loop algebra
at a three parameter family of auxiliary matrices
is constructed. The elements of this family satisfy a functional relation with
the transfer matrix allowing one to solve the eigenvalue problem of the model
and to derive the Bethe ansatz equations. This functional relation is obtained
from the decomposition of a tensor product of evaluation representations and
involves auxiliary matrices with different parameters. Because of this
dependence on additional parameters the auxiliary matrices break in general the
finite symmetries of the six-vertex model, such as spin-reversal or spin
conservation. More importantly, they also lift the extra degeneracies of the
transfer matrix due to the loop symmetry present at rational coupling values.
The extra parameters in the auxiliary matrices are shown to be directly related
to the elements in the enlarged center of the quantum loop algebra
at . This connection provides a geometric
interpretation of the enhanced symmetry of the six-vertex model at rational
coupling. The parameters labelling the auxiliary matrices can be interpreted as
coordinates on a three-dimensional complex hypersurface which remains invariant
under the action of an infinite-dimensional group of analytic transformations,
called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references
adde
Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
We connect two alternative concepts of solving integrable models, Baxter's
method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz.
The main steps of the calculation are performed in a general setting and a
formula for the Bethe eigenvalues of the Q-operator is derived. A proof is
given for states which contain up to three Bethe roots. Further evidence is
provided by relating the findings to the six-vertex fusion hierarchy. For the
XXZ spin-chain we analyze the cases when the deformation parameter of the
underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
Perfection of materials technology for producing improved Gunn-effect devices Interim scientific report
Chemical vapor deposition of epitaxial gallium arsenid
Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
We discuss an algebraic method for constructing eigenvectors of the transfer
matrix of the eight vertex model at the discrete coupling parameters. We
consider the algebraic Bethe ansatz of the elliptic quantum group for the case where the parameter satisfies for arbitrary integers , and . When or
is odd, the eigenvectors thus obtained have not been discussed previously.
Furthermore, we construct a family of degenerate eigenvectors of the XYZ spin
chain, some of which are shown to be related to the loop algebra
symmetry of the XXZ spin chain. We show that the dimension of some degenerate
eigenspace of the XYZ spin chain on sites is given by , if
is an even integer. The construction of eigenvectors of the transfer matrices
of some related IRF models is also discussed.Comment: 19 pages, no figure (revisd version with three appendices
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