14,604 research outputs found
Corner transfer matrices in statistical mechanics
Corner transfer matrices are a useful tool in the statistical mechanics of
simple two-dimensinal models. They can be very effective way of obtaining
series expansions of unsolved models, and of calculating the order parameters
of solved ones. Here we review these features and discuss the reason why the
method fails to give the order parameter of the chiral Potts model.Comment: 18 pages, 4 figures, for Proceedings of Conference on Symmetries and
Integrability of Difference Equations. (SIDE VII), Melbourne, July 200
Free field constructions for the elliptic algebra and Baxter's eight-vertex model
Three examples of free field constructions for the vertex operators of the
elliptic quantum group are obtained. Two of these
(for ) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
-algebra of Lepowsky and Wilson. The third one () is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at , however, is not related to the deformed
Virasoro algebra. Using these free field constructions, an integral formula for
the correlation functions of Baxter's eight-vertex model is obtained. This
formula shows different structure compared with the one obtained by Lashkevich
and Pugai.Comment: 23 pages. Based on talks given at "MATHPHYS ODYSSEY 2001-Integrable
Models and Beyond" at Okayama and Kyoto, February 19-23, 2001, et
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
A computer solution for the dynamic load, lubricant film thickness, and surface temperatures in spiral-bevel gears
A computer method for determining the dynamic load between spiral bevel pinion and gear teeth contact along the path of contact is described. The dynamic load analysis governs both the surface temperature and film thickness. Computer methods for determining the surface temperature, and film thickness are presented along with results obtained for a pair of typical spiral bevel gears
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
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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