4,174 research outputs found
Painlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point
We consider quantum correlation functions of the antiferromagnetic
spin- Heisenberg XXZ spin chain in a magnetic field. We show that
for a magnetic field close to the critical field (for the critical
magnetic field the ground state is ferromagnetic) certain correlation functions
can be expressed in terms of the solution of the Painlev\'e V transcendent.
This establishes a relation between solutions of Painlev\'e differential
equations and quantum correlation functions in models of {\sl interacting}
fermions. Painlev\'e transcendents were known to describe correlation functions
in models with free fermionic spectra.Comment: 10 pages, LaTeX2
Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain
We consider the paramagnetic phase of the random transverse-field Ising spin
chain and study the dynamical properties by numerical methods and scaling
considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to
new quantities, such as the non-linear susceptibility, higher excitations and
the energy-density autocorrelation function. We show that in the Griffiths
phase all the above quantities exhibit power-law singularities and the
corresponding critical exponents, which vary with the distance from the
critical point, can be related to the dynamical exponent z, the latter being
the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin
autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the
average energy-density autocorrelations decay with another exponent as
[G^e]_av(t)~t^{-2-1/z}.Comment: 8 pages RevTeX, 8 eps-figures include
Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases
The real-space renormalization group (RG) treatment of random
transverse-field Ising spin chains by Fisher ({\it Phys. Rev. B{\bf 51}, 6411
(1995)}) has been extended into the strongly ordered and strongly disordered
Griffiths phases and asymptotically exact results are obtained. In the
non-critical region the asymmetry of the renormalization of the couplings and
the transverse fields is related to a non-linear quantum control parameter,
, which is a natural measure of the distance from the quantum critical
point. , which is found to stay invariant along the RG trajectories and
has been expressed by the initial disorder distributions, stands in the
singularity exponents of different physical quantities (magnetization,
susceptibility, specific heat, etc), which are exactly calculated. In this way
we have observed a weak-universality scenario: the Griffiths-McCoy
singularities does not depend on the form of the disorder, provided the
non-linear quantum control parameter has the same value. The exact scaling
function of the magnetization with a small applied magnetic field is calculated
and the critical point magnetization singularity is determined in a simple,
direct way.Comment: 11 page
Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in and evolving by
a class of constrained surface diffusion flows. Our result, similar to earlier
results for the Willmore flow, gives both a positive lower bound on the time
for which a smooth solution exists, and a small upper bound on a power of the
total curvature during this time. By phrasing the theorem in terms of the
concentration of curvature in the initial surface, our result holds for very
general initial data and has applications to further development in asymptotic
analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1201.657
Magnetic friction in Ising spin systems
A new contribution to friction is predicted to occur in systems with magnetic
correlations: Tangential relative motion of two Ising spin systems pumps energy
into the magnetic degrees of freedom. This leads to a friction force
proportional to the area of contact. The velocity and temperature dependence of
this force are investigated. Magnetic friction is strongest near the critical
temperature, below which the spin systems order spontaneously.
Antiferromagnetic coupling leads to stronger friction than ferromagnetic
coupling with the same exchange constant. The basic dissipation mechanism is
explained. If the coupling of the spin system to the heat bath is weak, a
surprising effect is observed in the ordered phase: The relative motion acts
like a heat pump cooling the spins in the vicinity of the friction surface.Comment: 4 pages, 4 figure
Rejoinder to the Response arXiv:0812.2330 to 'Comment on a recent conjectured solution of the three-dimensional Ising model'
We comment on Z. D. Zhang's Response [arXiv:0812.2330] to our recent Comment
[arXiv:0811.3876] addressing the conjectured solution of the three-dimensional
Ising model reported in [arXiv:0705.1045].Comment: 2 page
Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings
The dynamical properties at T=0 of the one-dimensional (1D) s=1/2
nearest-neighbor (nn) XXZ model with an additional isotropic
next-nearest-neighbor (nnn) coupling are investigated by means of the recursion
method in combination with techniques of continued-fraction analysis. The focus
is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega),
which describe (for q=\pi) the fluctuations of the N\'eel and dimer order
parameters, respectively. We calculate (via weak-coupling continued-fraction
analysis) the dependence on the exchange constants of the infrared exponent,
the renormalized bandwidth of spinon excitations, and the spectral-weight
distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the
spin-fluid phase, which is realized for planar anisotropy and sufficiently
weak nnn coupling. For some parameter values we find a discrete branch of
excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but
not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from
author
Density Profiles in Random Quantum Spin Chains
We consider random transverse-field Ising spin chains and study the
magnetization and the energy-density profiles by numerically exact calculations
in rather large finite systems (). Using different boundary
conditions (free, fixed and mixed) the numerical data collapse to scaling
functions, which are very accurately described by simple analytic expressions.
The average magnetization profiles satisfy the Fisher-de Gennes scaling
conjecture and the corresponding scaling functions are indistinguishable from
those predicted by conformal invariance.Comment: 4 pages RevTeX, 4 eps-figures include
A cryogenic liquid-mirror telescope on the moon to study the early universe
We have studied the feasibility and scientific potential of zenith observing
liquid mirror telescopes having 20 to 100 m diameters located on the moon. They
would carry out deep infrared surveys to study the distant universe and follow
up discoveries made with the 6 m James Webb Space Telescope (JWST), with more
detailed images and spectroscopic studies. They could detect objects 100 times
fainter than JWST, observing the first, high-red shift stars in the early
universe and their assembly into galaxies. We explored the scientific
opportunities, key technologies and optimum location of such telescopes. We
have demonstrated critical technologies. For example, the primary mirror would
necessitate a high-reflectivity liquid that does not evaporate in the lunar
vacuum and remains liquid at less than 100K: We have made a crucial
demonstration by successfully coating an ionic liquid that has negligible vapor
pressure. We also successfully experimented with a liquid mirror spinning on a
superconducting bearing, as will be needed for the cryogenic, vacuum
environment of the telescope. We have investigated issues related to lunar
locations, concluding that locations within a few km of a pole are ideal for
deep sky cover and long integration times. We have located ridges and crater
rims within 0.5 degrees of the North Pole that are illuminated for at least
some sun angles during lunar winter, providing power and temperature control.
We also have identified potential problems, like lunar dust. Issues raised by
our preliminary study demand additional in-depth analyses. These issues must be
fully examined as part of a scientific debate we hope to start with the present
article.Comment: 35 pages, 11 figures. To appear in Astrophysical Journal June 20 200
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