497 research outputs found
Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to . With a view to establishing an exact
representation of the ground state of the finite size XXZ spin chain in terms
of elementary functions, we concentrate on the crossing-parameter
dependence around for which there is a known solution. The
approach taken involves the use of a physical solution of Baxter's t-Q
equation, corresponding to the ground state, as well as a non-physical solution
of the same equation. The calculation of and then of the ground state
derivative is covered. Possible applications of this derivative to the theory
of percolation have yet to be investigated. As far as the finite XXZ spin chain
with periodic boundary conditions is concerned, we find a similar solution for
an assymetric case which corresponds to the 6-vertex model with a special
magnetic field. For this case we find the analytic value of the ``magnetic
moment'' of the system in the corresponding state.Comment: 12 pages, latex, no figure
Free energies and critical exponents of the A_1^{(1)}, B_n^{(1)}, C_n^{(1)} and D_n^{(1)} face models
We obtain the free energies and critical exponents of models associated with
elliptic solutions of the star-triangle relation and reflection equation. The
models considered are related to the affine Lie algebras A_1^{(1)},
B_n^{(1)},C_n^{(1)} and D_n^{(1)}. The bulk and surface specific heat exponents
are seen to satisfy the scaling relation 2\alpha_s = \alpha_b + 2. It follows
from scaling relations that in regime III the correlation length exponent \nu
is given by \nu=(l+g)/2g, where l is the level and g is the dual Coxeter
number. In regime II we find \nu=(l+g)/2l.Comment: 9 pages, Latex, no figure
Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to .Comment: 6 page
Auxiliary matrices on both sides of the equator
The spectra of previously constructed auxiliary matrices for the six-vertex
model at roots of unity are investigated for spin-chains of even and odd
length. The two cases show remarkable differences. In particular, it is shown
that for even roots of unity and an odd number of sites the eigenvalues contain
two linear independent solutions to Baxter's TQ-equation corresponding to the
Bethe ansatz equations above and below the equator. In contrast, one finds for
even spin-chains only one linear independent solution and complete strings. The
other main result is the proof of a previous conjecture on the degeneracies of
the six-vertex model at roots of unity. The proof rests on the derivation of a
functional equation for the auxiliary matrices which is closely related to a
functional equation for the eight-vertex model conjectured by Fabricius and
McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some
typos correcte
The Importance of being Odd
In this letter I consider mainly a finite XXZ spin chain with periodic
boundary conditions and \bf{odd} \rm number of sites. This system is described
by the Hamiltonian . As it turned out, its ground state
energy is exactly proportional to the number of sites for a special
value of the asymmetry parameter . The trigonometric polynomial
, zeroes of which being the parameters of the ground state Bethe
eigenvector is explicitly constructed. This polynomial of degree
satisfy the Baxter T-Q equation. Using the second independent solution of this
equation corresponding to the same eigenvalue of the transfer matrix, it is
possible to find a derivative of the ground state energy w.r.t. the asymmetry
parameter. This derivative is closely connected with the correlation function
. In its turn this correlation
function is related to an average number of spin strings for the ground state
of the system under consideration: . I would like
to stress once more that all these simple formulas are \bf wrong \rm in the
case of even number of sites. Exactly this case is usually considered.Comment: 9 pages, based on the talk given at NATO Advanced Research Workshop
"Dynamical Symmetries in Integrable Two-dimensional Quantum Field Theories
and Lattice Models", 25-30 September 2000, Kyiv, Ukraine. New references are
added plus some minor correction
The transmission of nosocomial pathogens in an intensive care unit: a space–time clustering and structural equation modelling approach
We investigated the incidence of cases of nosocomial pathogens and risk factors in an intensive treatment unit ward to determine if the number of cases is dependent on location of patients and the colonization/infection history of the ward. A clustering approach method was developed to investigate the patterns of spread of cases through time for five microorganisms [methicillin-resistant Staphylococcus aureus (MRSA), Acinetobacter spp., Klebsiella spp., Candida spp., and Pseudomonas aeruginosa] using hospital microbiological monitoring data and ward records of patient-bed use. Cases of colonization/infection by MRSA, Candida and Pseudomonas were clustered in beds and through time while cases of Klebsiella and Acinetobacter were not. We used structural equation modelling to analyse interacting risk factors and the potential pathways of transmission in the ward. Prior nurse contact with colonized/infected patients, mediated by the number of patient-bed movements, were important predictors for all cases, except for those of Pseudomonas. General health and invasive surgery were significant predictors of cases of Candida and Klebsiella. We suggest that isolation and bed movement as a strategy to manage MRSA infections is likely to impact upon the incidence of cases of other opportunist pathogen
Switching kinetics of ferroelectric polymer nanomesas
The switching dynamics and switching time of ferroelectric nanomesas grown from the paraelectric phase of ultrathin Langmuir–Blodgett vinylidene fluoride and trifluoroethylene copolymer films are investigated. Ferroelectric nanomesas are created through heat treatment and self-organization and have an average height of 10 nm and an average diameter of 100 nm. Ferroelectric nanomesas are highly crystalline and are in the ferroelectric phase and switch faster than 50 μs. The dependence of switching time on applied voltage implies an extrinsic switching nature
Optical second harmonic generation probe of two-dimensional ferroelectricity
Optical second harmonic generation (SHG) is used as a noninvasive probe of
two-dimensional (2D) ferroelectricity in Langmuir-Blodgett (LB) films of
copolymer vinylidene fluoride with trifluorethylene. The surface 2D
ferroelectric-paraelectric phase transition in the topmost layer of LB films
and a thickness independent (almost 2D) transition in the bulk of these films
are observed in temperature studies of SHG.Comment: 9 pages, 2 figures, Optics Letters, in prin
Polarization switching at the nanoscale in ferroelectric copolymer thin films
The polarization switching kinetics were measured at the nanoscale in continuous thin films of a ferroelectric copolymer of vinylidene fluoride and trifluoroethylene. The dependence of the switching rate on voltage for a 54-nm thick film exhibits extrinsic nucleation and domain-growth type kinetics with no true threshold coercive field, and is qualitatively different from the behavior of an 18-nm thick film, which exhibits intrinsic switching kinetics, and a true threshold field. The results are consistent with studies of thin film capacitors of much larger area and with a recent refinement of the theory of the critical size for intrinsic switching
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