7,484 research outputs found
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
Bethe Equations "on the Wrong Side of Equator"
We analyse the famous Baxter's equations for () spin chain
and show that apart from its usual polynomial (trigonometric) solution, which
provides the solution of Bethe-Ansatz equations, there exists also the second
solution which should corresponds to Bethe-Ansatz beyond . This second
solution of Baxter's equation plays essential role and together with the first
one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
In this paper, we construct a Q-operator as a trace of a representation of
the universal R-matrix of over an infinite-dimensional
auxiliary space. This auxiliary space is a four-parameter generalization of the
q-oscillator representations used previously. We derive generalized T-Q
relations in which 3 of these parameters shift. After a suitable restriction of
parameters, we give an explicit expression for the Q-operator of the 6-vertex
model and show the connection with Baxter's expression for the central block of
his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that
includes a simple explicit expression for the Q matrix for the 6-vertex mode
Tetromino tilings and the Tutte polynomial
We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each
tile is assigned a weight that depends on its orientation and position on the
lattice. For a particular choice of the weights, the generating function of
tilings is shown to be the evaluation of the multivariate Tutte polynomial
Z\_G(Q,v) (known also to physicists as the partition function of the Q-state
Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the
edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure
The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three dimensional Lenard-Jones fluids
We analyze the interrelation between the coexistence curve of the
Lennard-Jones fluid and the Ising model in two and three dimensions within the
global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B
\textbf{114} 2852 (2010)]. In case of two dimensions we use the exact Onsager
result to construct the binodal of the corresponding Lennard-Jones fluid and
compare it with the results of the simulations. In the three dimensional case
we use available numerical results for the Ising model for the corresponding
mapping. The possibility to observe the singularity of the binodal diameter is
discussed.Comment: 9 pages, 2 figure
Status report on the Low Energy Neutron Source for 2015
The Low Energy Neutron Source at Indiana University first produced cold neutrons in April of 2005. Ten years after first reaching this milestone, the facility has three instruments in operation on its cold target station, and a second target station is devoted to thermal and fast neutron physics offers capabilities in radiation effects research (single-event effects in electronics) and radiography. Key elements in our success over these last ten years have been the diversity of activities we have been able maintain (which often involves using each of our instruments for multiple different activities), the close relationship we have developed with a number of major sources, and the focus we have had on innovation in neutron
instrumentation. In this presentation, we will introduce some of the highlights from our most recent activities, provide an update on some of our technical challenges, and describe some of our ideas for the future
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
Directed-loop Monte Carlo simulations of vertex models
We show how the directed-loop Monte Carlo algorithm can be applied to study
vertex models. The algorithm is employed to calculate the arrow polarization in
the six-vertex model with the domain wall boundary conditions (DWBC). The model
exhibits spatially separated ordered and ``disordered'' regions. We show how
the boundary between these regions depends on parameters of the model. We give
some predictions on the behavior of the polarization in the thermodynamic limit
and discuss the relation to the Arctic Circle theorem.Comment: Extended version with autocorrelations and more figures. Added 2
reference
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