484 research outputs found
Bethe Equation of -model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
We establish the Bethe equation of the -model in the -state
chiral Potts model (including the degenerate selfdual cases) with alternating
vertical rapidities. The eigenvalues of a finite-size transfer matrix of the
chiral Potts model are computed by use of functional relations. The
significance of the "alternating superintegrable" case of the chiral Potts
model is discussed, and the degeneracy of -model found as in the
homogeneous superintegrable chiral Potts model.Comment: Latex 25 pages; Typos corrected, Minor changes for clearer
presentation, References added-Journal versio
Duality and Symmetry in Chiral Potts Model
We discover an Ising-type duality in the general -state chiral Potts
model, which is the Kramers-Wannier duality of planar Ising model when N=2.
This duality relates the spectrum and eigenvectors of one chiral Potts model at
a low temperature (of small ) to those of another chiral Potts model at a
high temperature (of ). The -model and chiral Potts model
on the dual lattice are established alongside the dual chiral Potts models.
With the aid of this duality relation, we exact a precise relationship between
the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts
model and the -loop-algebra symmetry of its associated
spin- XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are
corrected with minor changes in expression of some formula
On -model in Chiral Potts Model and Cyclic Representation of Quantum Group
We identify the precise relationship between the five-parameter
-family in the -state chiral Potts model and XXZ chains with
-cyclic representation. By studying the Yang-Baxter relation of the
six-vertex model, we discover an one-parameter family of -operators in terms
of the quantum group . When is odd, the -state
-model can be regarded as the XXZ chain of
cyclic representations with . The symmetry algebra of the
-model is described by the quantum affine algebra via the canonical representation. In general for an arbitrary
, we show that the XXZ chain with a -cyclic representation for
is equivalent to two copies of the same -state
-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer
presentation, References added and updated-Journal versio
The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity for odd N
Following Baxter's method of producing Q_{72}-operator, we construct the
Q-operator of the root-of-unity eight-vertex model for the crossing parameter
with odd where Q_{72} does not exist. We use this
new Q-operator to study the functional relations in the Fabricius-McCoy
comparison between the root-of-unity eight-vertex model and the superintegrable
N-state chiral Potts model. By the compatibility of the constructed Q-operator
with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we
verify the set of functional relations of the root-of-unity eight-vertex model
using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation,
References added and updated-Journal versio
The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
We construct the explicit -operator incorporated with the
-loop-algebra symmetry of the six-vertex model at roots of unity. The
functional relations involving the -operator, the six-vertex transfer matrix
and fusion matrices are derived from the Bethe equation, parallel to the
Onsager-algebra-symmetry discussion in the superintegrable -state chiral
Potts model. We show that the whole set of functional equations is valid for
the -operator. Direct calculations in certain cases are also given here for
clearer illustration about the nature of the -operator in the symmetry study
of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations
added for clearer presentation, References updated-Journal version with
modified labelling of sections and formula
The Onsager Algebra Symmetry of -matrices in the Superintegrable Chiral Potts Model
We demonstrate that the -matrices in the superintegrable chiral
Potts model possess the Onsager algebra symmetry for their degenerate
eigenvalues. The Fabricius-McCoy comparison of functional relations of the
eight-vertex model for roots of unity and the superintegrable chiral Potts
model has been carefully analyzed by identifying equivalent terms in the
corresponding equations, by which we extract the conjectured relation of
-operators and all fusion matrices in the eight-vertex model corresponding
to the -relation in the chiral Potts model.Comment: Latex 21 pages; Typos added, References update
Individuals' Use of Care While Uninsured: Effects of Time Since Episode Inception and Episode Length
Few studies have addressed how use of care may vary over the course of an episode of being uninsured or across uninsured episodes of varying duration. This research models the probability that an uninsured individual has (a) any medical expenditures or charges, and (b) any office-based visit during each month of an uninsured episode. We find that the ultimate length of an individual's episode of being uninsured bears relatively little on individuals' use of healthcare in any particular month and that the probability of health care utilization rises during the first year of the episode, with more use in the second six months of the year compared to the first six months.
CHIP Expansions to Higher-Income Children in Three States: Profiles of Eligibility and Insurance Coverage
Summarizes findings on how changes in eligibility rules for children's public health insurance programs affected 2002-09 coverage rates and the number of uninsured children in Illinois, Pennsylvania, and Washington. Compares results by scope of reform
Take-Up of Public Insurance and Crowd-out of Private Insurance Under Recent CHIP Expansions to Higher Income Children
We analyze the effects of states’ expansions of CHIP eligibility to children in higher income families during 2002-2009 on take-up of public coverage, crowd-out of private coverage, and rates of uninsurance. Our results indicate these expansions were associated with limited uptake of public coverage and only a two percentage point reduction in the uninsurance rate among these children. Because not all of the take-up of public insurance among eligible children is accounted for by children who transfer from being uninsured to having public insurance, our results suggest that there may be some crowd-out of private insurance coverage; the upper bound crowd-out rate we calculate is 46 percent.
Fusion Operators in the Generalized -model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
We construct the fusion operators in the generalized -model using
the fused -operators, and verify the fusion relations with the truncation
identity. The algebraic Bethe ansatz discussion is conducted on two special
classes of which include the superintegrable chiral Potts model.
We then perform the parallel discussion on the XXZ spin chain at roots of
unity, and demonstrate that the -loop-algebra symmetry exists for the
root-of-unity XXZ spin chain with a higher spin, where the evaluation
parameters for the symmetry algebra are identified by the explicit
Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the
comparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by
adding explanations for better presentation. Terminology in the content and
the title refined. References added and updated-Journal versio
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