19,475 research outputs found
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
Negative-weight percolation
We describe a percolation problem on lattices (graphs, networks), with edge
weights drawn from disorder distributions that allow for weights (or distances)
of either sign, i.e. including negative weights. We are interested whether
there are spanning paths or loops of total negative weight. This kind of
percolation problem is fundamentally different from conventional percolation
problems, e.g. it does not exhibit transitivity, hence no simple definition of
clusters, and several spanning paths/loops might coexist in the percolation
regime at the same time. Furthermore, to study this percolation problem
numerically, one has to perform a non-trivial transformation of the original
graph and apply sophisticated matching algorithms.
Using this approach, we study the corresponding percolation transitions on
large square, hexagonal and cubic lattices for two types of disorder
distributions and determine the critical exponents. The results show that
negative-weight percolation is in a different universality class compared to
conventional bond/site percolation. On the other hand, negative-weight
percolation seems to be related to the ferromagnet/spin-glass transition of
random-bond Ising systems, at least in two dimensions.Comment: v1: 4 pages, 4 figures; v2: 10 pages, 7 figures, added results, text
and reference
Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2
Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses
Unbiased samples of ground states were generated for the short-range Ising
spin glass with Jij=+/-1, in three dimensions. Clustering the ground states
revealed their hierarchical structure, which is explained by correlated spin
domains, serving as cores for macroscopic zero energy "excitations".Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let
A new method for analyzing ground-state landscapes: ballistic search
A ``ballistic-search'' algorithm is presented which allows the identification
of clusters (or funnels) of ground states in Ising spin glasses even for
moderate system sizes. The clusters are defined to be sets of states, which are
connected in state-space by chains of zero-energy flips of spins. The technique
can also be used to estimate the sizes of such clusters. The performance of the
method is tested with respect to different system sizes and choices of
parameters. As an application the ground-state funnel structure of
two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by
calculating a huge number of ground states per realization. A T=0 entropy per
spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte
Reply to the Comment on `Glassy Transition in a Disordered Model for the RNA Secondary Structure'
We reply to the Comment by Hartmann (cond-mat/9908132) on our paper Phys.
Rev. Lett. 84 (2000) 2026 (also cond-mat/9907125).Comment: 1 page, no figures. Accepted for publication in Phys. Rev. Let
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
Lower Critical Dimension of Ising Spin Glasses
Exact ground states of two-dimensional Ising spin glasses with Gaussian and
bimodal (+- J) distributions of the disorder are calculated using a
``matching'' algorithm, which allows large system sizes of up to N=480^2 spins
to be investigated. We study domain walls induced by two rather different types
of boundary-condition changes, and, in each case, analyze the system-size
dependence of an appropriately defined ``defect energy'', which we denote by
DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with
\theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition
changes. These results are in reasonable agreement with each other, allowing
for small systematic effects. They also agree well with earlier work on smaller
sizes. The negative value indicates that two dimensions is below the lower
critical dimension d_c. For the +-J model, we obtain a different result, namely
the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta
= 0, indicating that the lower critical dimension for the +-J model exactly
d_c=2.Comment: 4 pages, 4 figures, 1 table, revte
Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm
We developed a genetic algorithm (GA) in the Heisenberg model that combines a
triadic crossover and a parameter-free genetic algorithm. Using the algorithm,
we examined the ground-state stiffness of the Heisenberg model in three
dimensions up to a moderate size range. Results showed the stiffness constant
of in the periodic-antiperiodic boundary condition method and that
of in the open-boundary-twist method. We considered the
origin of the difference in between the two methods and suggested that
both results show the same thing: the ground state of the open system is stable
against a weak perturbation.Comment: 11 pages, 5 figure
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