5,962 research outputs found
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
Hard hexagon partition function for complex fugacity
We study the analyticity of the partition function of the hard hexagon model
in the complex fugacity plane by computing zeros and transfer matrix
eigenvalues for large finite size systems. We find that the partition function
per site computed by Baxter in the thermodynamic limit for positive real values
of the fugacity is not sufficient to describe the analyticity in the full
complex fugacity plane. We also obtain a new algebraic equation for the low
density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using
PDFLaTeX. Some minor changes added to version 2 in response to referee
report
Integrability vs non-integrability: Hard hexagons and hard squares compared
In this paper we compare the integrable hard hexagon model with the
non-integrable hard squares model by means of partition function roots and
transfer matrix eigenvalues. We consider partition functions for toroidal,
cylindrical, and free-free boundary conditions up to sizes and
transfer matrices up to 30 sites. For all boundary conditions the hard squares
roots are seen to lie in a bounded area of the complex fugacity plane along
with the universal hard core line segment on the negative real fugacity axis.
The density of roots on this line segment matches the derivative of the phase
difference between the eigenvalues of largest (and equal) moduli and exhibits
much greater structure than the corresponding density of hard hexagons. We also
study the special point of hard squares where all eigenvalues have unit
modulus, and we give several conjectures for the value at of the
partition functions.Comment: 46 page
Design of the software development and verification system (SWDVS) for shuttle NASA study task 35
An overview of the Software Development and Verification System (SWDVS) for the space shuttle is presented. The design considerations, goals, assumptions, and major features of the design are examined. A scenario that shows three persons involved in flight software development using the SWDVS in response to a program change request is developed. The SWDVS is described from the standpoint of different groups of people with different responsibilities in the shuttle program to show the functional requirements that influenced the SWDVS design. The software elements of the SWDVS that satisfy the requirements of the different groups are identified
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
Randomly incomplete spectra and intermediate statistics
By randomly removing a fraction of levels from a given spectrum a model is
constructed that describes a crossover from this spectrum to a Poisson
spectrum. The formalism is applied to the transitions towards Poisson from
random matrix theory (RMT) spectra and picket fence spectra. It is shown that
the Fredholm determinant formalism of RMT extends naturally to describe
incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review
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
Steady States of a Nonequilibrium Lattice Gas
We present a Monte Carlo study of a lattice gas driven out of equilibrium by
a local hopping bias. Sites can be empty or occupied by one of two types of
particles, which are distinguished by their response to the hopping bias. All
particles interact via excluded volume and a nearest-neighbor attractive force.
The main result is a phase diagram with three phases: a homogeneous phase, and
two distinct ordered phases. Continuous boundaries separate the homogeneous
phase from the ordered phases, and a first-order line separates the two ordered
phases. The three lines merge in a nonequilibrium bicritical point.Comment: 14 pages, 24 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
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