10,753 research outputs found
A study of cross sections for excitation of pseudostates
Using the electron-hydrogen scattering Temkin-Poet model we investigate the
behavior of the cross sections for excitation of all of the states used in the
convergent close-coupling (CCC) formalism. In the triplet channel, it is found
that the cross section for exciting the positive-energy states is approximately
zero near-threshold and remains so until a further energy, equal to the energy
of the state, is added to the system. This is consistent with the step-function
hypothesis [Bray, Phys. Rev. Lett. {\bf 78} 4721 (1997)] and inconsistent with
the expectations of Bencze and Chandler [Phys. Rev. A {\bf 59} 3129 (1999)].
Furthermore, we compare the results of the CCC-calculated triplet and singlet
single differential cross sections with the recent benchmark results of
Baertschy et al. [Phys. Rev. A (to be published)], and find consistent
agreement.Comment: Four pages, 5 figure
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
On the number of metastable states in spin glasses
In this letter, we show that the formulae of Bray and Moore for the average
logarithm of the number of metastable states in spin glasses can be obtained by
calculating the partition function with coupled replicas with the symmetry
among these explicitly broken according to a generalization of the `two-group'
ansatz. This equivalence allows us to find solutions of the BM equations where
the lower `band-edge' free energy equals the standard static free energy. We
present these results for the Sherrington-Kirkpatrick model, but we expect them
to apply to all mean-field spin glasses.Comment: 6 pages, LaTeX, no figures. Postscript directly available
http://chimera.roma1.infn.it/index_papers_complex.htm
Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter
Corrections to scaling, associated with deviations of the order parameter
from the scaling morphology in the initial state, are studied for systems with
O(n) symmetry at zero temperature in phase-ordering kinetics. Including
corrections to scaling, the equal-time pair correlation function has the form
C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length
scale. The correction-to-scaling exponent, omega, and the correction-to-scaling
function, f_1(x), are calculated for both nonconserved and conserved order
parameter systems using the approximate Gaussian closure theory of Mazenko. In
general, omega is a non-trivial exponent which depends on both the
dimensionality, d, of the system and the number of components, n, of the order
parameter. Corrections to scaling are also calculated for the nonconserved 1-d
XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure
Velocity Distribution of Topological Defects in Phase-Ordering Systems
The distribution of interface (domain-wall) velocities in a
phase-ordering system is considered. Heuristic scaling arguments based on the
disappearance of small domains lead to a power-law tail,
for large v, in the distribution of . The exponent p is
given by , where d is the space dimension and 1/z is the growth
exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the
conserved case (model B). The nonconserved result is exemplified by an
approximate calculation of the full distribution using a gaussian closure
scheme. The heuristic arguments are readily generalized to conserved case
(model B). The nonconserved result is exemplified by an approximate calculation
of the full distribution using a gaussian closure scheme. The heuristic
arguments are readily generalized to systems described by a vector order
parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear
in Physical Review E (May 1, 1997
Vortex annihilation in the ordering kinetics of the O(2) model
The vortex-vortex and vortex-antivortex correlation functions are determined
for the two-dimensional O(2) model undergoing phase ordering. We find
reasonably good agreement with simulation results for the vortex-vortex
correlation function where there is a short-scaled distance depletion zone due
to the repulsion of like-signed vortices. The vortex-antivortex correlation
function agrees well with simulation results for intermediate and long-scaled
distances. At short-scaled distances the simulations show a depletion zone not
seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.
The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work
to that of Newman and Stei
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
Evidence for existence of many pure ground states in 3d Spin Glasses
Ground states of 3d EA Ising spin glasses are calculated for sizes up to
using a combination of genetic algorithms and cluster-exact
approximation . The distribution of overlaps is calculated. For
increasing size the width of converges to a nonzero value, indicating
that many pure ground states exist for short range Ising spin glasses.Comment: 4 pages, 3 figures, 2 tables, 16 reference
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