8,008 research outputs found
Stress relaxation and mechanical properties of RL-1973 and PD-200-16 silicone resin sponge materials
Stress relaxation tests were conducted by loading specimens in double-lap shear to a preselected strain level and monitoring the decay of stress with time. The stress relaxation response characteristics were measured over a temperature range of 100 to 300 K and four strain levels. It is concluded that only a slight amount of stress relaxation was observed, and the stiffness increased approximately two orders of magnitude over the range of temperatures
Painleve versus Fuchs
The sigma form of the Painlev{\'e} VI equation contains four arbitrary
parameters and generically the solutions can be said to be genuinely
``nonlinear'' because they do not satisfy linear differential equations of
finite order. However, when there are certain restrictions on the four
parameters there exist one parameter families of solutions which do satisfy
(Fuchsian) differential equations of finite order. We here study this phenomena
of Fuchsian solutions to the Painlev{\'e} equation with a focus on the
particular PVI equation which is satisfied by the diagonal correlation function
C(N,N) of the Ising model. We obtain Fuchsian equations of order for
C(N,N) and show that the equation for C(N,N) is equivalent to the
symmetric power of the equation for the elliptic integral .
We show that these Fuchsian equations correspond to rational algebraic curves
with an additional Riccati structure and we show that the Malmquist Hamiltonian
variables are rational functions in complete elliptic integrals. Fuchsian
equations for off diagonal correlations are given which extend our
considerations to discrete generalizations of Painlev{\'e}.Comment: 18 pages, Dedicated to the centenary of the publication of the
Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de
Paris by Richard Fuchs in 190
SCOZA for Monolayer Films
We show the way in which the self-consistent Ornstein-Zernike approach
(SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian
models can best be applied to two-dimensional systems such as thin films. We
use the nearest-neighbor lattice gas on a square lattice as an illustrative
example.Comment: 10 pages, 5 figure
The importance of the Ising model
Understanding the relationship which integrable (solvable) models, all of
which possess very special symmetry properties, have with the generic
non-integrable models that are used to describe real experiments, which do not
have the symmetry properties, is one of the most fundamental open questions in
both statistical mechanics and quantum field theory. The importance of the
two-dimensional Ising model in a magnetic field is that it is the simplest
system where this relationship may be concretely studied. We here review the
advances made in this study, and concentrate on the magnetic susceptibility
which has revealed an unexpected natural boundary phenomenon. When this is
combined with the Fermionic representations of conformal characters, it is
suggested that the scaling theory, which smoothly connects the lattice with the
correlation length scale, may be incomplete for .Comment: 33 page
Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
We study numerically the paramagnetic phase of the spin-1/2 random
transverse-field Ising chain, using a mapping to non-interacting fermions. We
extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and
to dynamical properties. Our results are consistent with the idea that there
are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a
continuously varying exponent , where measures the
deviation from criticality. There are some discrepancies between the values of
obtained from different quantities, but this may be due to
corrections to scaling. The average on-site time dependent correlation function
decays with a power law in the paramagnetic phase, namely
, where is imaginary time. However, the typical
value decays with a stretched exponential behavior, ,
where may be related to . We also obtain results for the full
probability distribution of time dependent correlation functions at different
points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical
time dependent correlation function has been greatly expanded. Other papers
of APY are available on-line at http://schubert.ucsc.edu/pete
The saga of the Ising susceptibility
We review developments made since 1959 in the search for a closed form for
the susceptibility of the Ising model. The expressions for the form factors in
terms of the nome and the modulus are compared and contrasted. The
generalized correlations are defined and explicitly
computed in terms of theta functions for .Comment: 19 pages, 1 figur
Ising Dynamics with Damping
We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality.Comment: 8 pages, 8 figures, 2 colum
High-precision estimate of g4 in the 2D Ising model
We compute the renormalized four-point coupling in the 2d Ising model using
transfer-matrix techniques. We greatly reduce the systematic uncertainties
which usually affect this type of calculations by using the exact knowledge of
several terms in the scaling function of the free energy. Our final result is
g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for
publication in Journal of Physics
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
Impurity spin relaxation in S=1/2 XX chains
Dynamic autocorrelations (\alpha=x,z) of an
isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin,
defined by a local change in the nearest-neighbor coupling, is either in the
bulk or at the boundary of the open-ended chain. The exact numerical
calculation of the correlations employs the Jordan-Wigner mapping from spin
operators to Fermi operators; effects of finite system size can be eliminated.
Two distinct temperature regimes are observed in the long-time asymptotic
behavior. At T=0 only power laws are present. At high T the x correlation
decays exponentially (except at short times) while the z correlation still
shows an asymptotic power law (different from the one at T=0) after an
intermediate exponential phase. The boundary impurity correlations follow power
laws at all T. The power laws for the z correlation and the boundary
correlations can be deduced from the impurity-induced changes in the properties
of the Jordan-Wigner fermion states.Comment: Final version to be published in Phys. Rev. B. Three references
added, extended discussion of relation to previous wor
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