39,478 research outputs found
Comment on "Evidence for nontrivial ground-state structure of 3d +/- J spin glasses"
In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented
results for the structure of the degenerate ground states of the
three-dimensional +/- J spin glass model obtained using a genetic algorithm. In
this Comment, I argue that the method does not produce the correct
thermodynamic distribution of ground states and therefore gives erroneous
results for the overlap distribution. I present results of simulated annealing
calculations using different annealing rates for cubic lattices with
N=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant
dependence on the annealing rate, even when the energy has converged. For fast
annealing, moments of the distribution are similar to those presented by
Hartmann. However, as the annealing rate is lowered, they approach the results
previously obtained using a multi-canonical Monte Carlo method. This shows
explicitly that care must be taken not only to reach states with the lowest
energy but also to ensure that they obey the correct thermodynamic
distribution, i.e., that the probability is the same for reaching any of the
ground states.Comment: 2 pages, Revtex, 1 PostScript figur
Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension
The disorder-driven phase transition of the RFIM is observed using exact
ground-state computer simulations for hyper cubic lattices in d=5,6,7
dimensions. Finite-size scaling analyses are used to calculate the critical
point and the critical exponents of the specific heat, magnetization,
susceptibility and of the correlation length. For dimensions d=6,7 which are
larger or equal to the assumed upper critical dimension, d_u=6, mean-field
behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis
of the numerical data, it appears to be necessary to include recently proposed
corrections to scaling at and beyond the upper critical dimension.Comment: 8 pages and 13 figures; A consise summary of this work can be found
in the papercore database at http://www.papercore.org/Ahrens201
Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
We study the correlated-disorder driven zero-temperature phase transition of
the Random-Field Ising Magnet using exact numerical ground-state calculations
for cubic lattices. We consider correlations of the quenched disorder decaying
proportional to r^a, where r is the distance between two lattice sites and a<0.
To obtain exact ground states, we use a well established mapping to the
graph-theoretical maximum-flow problem, which allows us to study large system
sizes of more than two million spins. We use finite-size scaling analyses for
values a={-1,-2,-3,-7} to calculate the critical point and the critical
exponents characterizing the behavior of the specific heat, magnetization,
susceptibility and of the correlation length close to the critical point. We
find basically the same critical behavior as for the RFIM with delta-correlated
disorder, except for the finite-size exponent of the susceptibility and for the
case a=-1, where the results are also compatible with a phase transition at
infinitesimal disorder strength.
A summary of this work can be found at the papercore database at
www.papercore.org.Comment: 9 pages, 13 figure
Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
We consider the negative weight percolation (NWP) problem on hypercubic
lattice graphs with fully periodic boundary conditions in all relevant
dimensions from d=2 to the upper critical dimension d=6. The problem exhibits
edge weights drawn from disorder distributions that allow for weights of either
sign. We are interested in in the full ensemble of loops with negative weight,
i.e. non-trivial (system spanning) loops as well as topologically trivial
("small") loops. The NWP phenomenon refers to the disorder driven proliferation
of system spanning loops of total negative weight. While previous studies where
focused on the latter loops, we here put under scrutiny the ensemble of small
loops. Our aim is to characterize -using this extensive and exhaustive
numerical study- the loop length distribution of the small loops right at and
below the critical point of the hypercubic setups by means of two independent
critical exponents. These can further be related to the results of previous
finite-size scaling analyses carried out for the system spanning loops. For the
numerical simulations we employed a mapping of the NWP model to a combinatorial
optimization problem that can be solved exactly by using sophisticated matching
algorithms. This allowed us to study here numerically exact very large systems
with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at
http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text
overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174
Interpolation and harmonic majorants in big Hardy-Orlicz spaces
Free interpolation in Hardy spaces is caracterized by the well-known Carleson
condition. The result extends to Hardy-Orlicz spaces contained in the scale of
classical Hardy spaces , . For the Smirnov and the Nevanlinna
classes, interpolating sequences have been characterized in a recent paper in
terms of the existence of harmonic majorants (quasi-bounded in the case of the
Smirnov class). Since the Smirnov class can be regarded as the union over all
Hardy-Orlicz spaces associated with a so-called strongly convex function, it is
natural to ask how the condition changes from the Carleson condition in
classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of
this paper is to narrow down this gap from the Smirnov class to ``big''
Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences
for a class of Hardy-Orlicz spaces that carry an algebraic structure and that
are strictly bigger than . It turns out that the
interpolating sequences are again characterized by the existence of
quasi-bounded majorants, but now the weights of the majorants have to be in
suitable Orlicz spaces. The existence of harmonic majorants in such Orlicz
spaces will also be discussed in the general situation. We finish the paper
with an example of a separated Blaschke sequence that is interpolating for
certain Hardy-Orlicz spaces without being interpolating for slightly smaller
ones.Comment: 19 pages, 2 figure
Few-Particle Effects in Semiconductor Quantum Dots: Observation of Multi-Charged-Excitons
We investigate experimentally and theoretically few-particle effects in the
optical spectra of single quantum dots (QDs). Photo-depletion of the QD
together with the slow hopping transport of impurity-bound electrons back to
the QD are employed to efficiently control the number of electrons present in
the QD. By investigating structurally identical QDs, we show that the spectral
evolutions observed can be attributed to intrinsic, multi-particle-related
effects, as opposed to extrinsic QD-impurity environment-related interactions.
From our theoretical calculations we identify the distinct transitions
related to excitons and excitons charged with up to five additional electrons,
as well as neutral and charged biexcitons.Comment: 4 pages, 4 figures, revtex. Accepted for publication in Physical
Review Letter
Derivation of effective spin models from a three band model for CuO_2-planes
The derivation of effective spin models describing the low energy magnetic
properties of undoped CuO_2-planes is reinvestigated. Our study aims at a
quantitative determination of the parameters of effective spin models from
those of a multi-band model and is supposed to be relevant to the analysis of
recent improved experimental data on the spin wave spectrum of La_2CuO_4.
Starting from a conventional three-band model we determine the exchange
couplings for the nearest and next-nearest neighbor Heisenberg exchange as well
as for 4- and 6-spin exchange terms via a direct perturbation expansion up to
12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping
t_pd. Our results demonstrate that this perturbation expansion does not
converge for hopping parameters of the relevant size. Well behaved
extrapolations of the couplings are derived, however, in terms of Pade
approximants. In order to check the significance of these results from the
direct perturbation expansion we employ the Zhang-Rice reformulation of the
three band model in terms of hybridizing oxygen Wannier orbitals centered at
copper ion sites. In the Wannier notation the perturbation expansion is
reorganized by an exact treatment of the strong site-diagonal hybridization.
The perturbation expansion with respect to the weak intersite hybridizations is
calculated up to 4th order for the Heisenberg coupling and up to 6th order for
the 4-spin coupling. It shows excellent convergence and the results are in
agreement with the Pade approximants of the direct expansion. The relevance of
the 4-spin coupling as the leading correction to the nearest neighbor
Heisenberg model is emphasized.Comment: 27 pages, 10 figures. Changed from particle to hole notation, right
value for the charge transfer gap used; this results in some changes in the
figures and a higher value of the ring exchang
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