22,993 research outputs found
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
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
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
A Systematic Analysis of Supernova Light in Gamma-Ray Burst Afterglows
We systematically reanalyzed all Gamma-Ray Burst (GRB) afterglow data
published through the end of 2002, in an attempt to detect the predicted
supernova light component and to gain statistical insight on its
phenomenological properties. We fit the observed photometric light curves as
the sum of an afterglow, an underlying host galaxy, and a supernova component.
The latter is modeled using published multi-color light curves of SN 1998bw as
a template. The total sample of afterglows with established redshifts contains
21 bursts (GRB 970228 - GRB 021211). For nine of these GRBs a weak supernova
excess (scaled to SN 1998bw) was found, what makes this to one of the first
samples of high-z core collapse supernovae. Among this sample are all bursts
with redshifts less than ~0.7. These results strongly support the notion that
in fact all afterglows of long-duration GRBs contain light from an associated
supernova. A statistics of the physical parameters of these GRB-supernovae
shows that SN 1998bw was at the bright end of its class, while it was not
special with respect to its light curve shape. Finally, we have searched for a
potential correlation of the supernova luminosities with the properties of the
corresponding bursts and optical afterglows, but we have not found such a
relation.Comment: 25 pages, 7 figures, accepted by ApJ; revised, shortened and updated
compared to version 1; Title slightly changed; all figures showing individual
afterglow light curves removed, as advised by the referee; conclusions
unchange
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
Mid-infrared observations of the SGR 1900+14 error box
We report on mid-infrared observations of the compact stellar cluster located
in the proximity of SGR 1900+14, and the radio/X-ray position of this
soft-gamma repeater. Observations were performed in May and June of 2001 when
the bursting source was in an active state. At the known radio and X-ray
position of the SGR we did not detect transient mid-IR activity, although the
observations were performed only hours before and after an outburst in the
high-energy band.Comment: 4 pages, 3 figures, to appear in "Gamma-Ray Burst and Afterglow
Astronomy 2001", Woods Hole; 5-9 Nov, 200
Anomalous latent heat in non-equilibrium phase transitions
We study first-order phase transitions in a two-temperature system, where due
to the time-scale separation all the basic thermodynamical quantities (free
energy, entropy, etc) are well-defined. The sign of the latent heat is found to
be counterintuitive: it is positive when going from the phase where the
temperatures and the entropy are higher to the one where these quantities are
lower. The effect exists only out of equilibrium and requires conflicting
interactions. It is displayed on a lattice gas model of ferromagnetically
interacting spin-1/2 particles.Comment: 4 pages, 2 figure
Reduction of Two-Dimensional Dilute Ising Spin Glasses
The recently proposed reduction method is applied to the Edwards-Anderson
model on bond-diluted square lattices. This allows, in combination with a
graph-theoretical matching algorithm, to calculate numerically exact ground
states of large systems. Low-temperature domain-wall excitations are studied to
determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found,
consistent with previous results obtained on undiluted lattices. This
comparison demonstrates the validity of the reduction method for bond-diluted
spin systems and provides strong support for similar studies proclaiming
accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see
http://www.physics.emory.edu/faculty/boettcher
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
Statistics of lowest excitations in two dimensional Gaussian spin glasses
A detailed investigation of lowest excitations in two-dimensional Gaussian
spin glasses is presented. We show the existence of a new zero-temperature
exponent lambda describing the relative number of finite-volume excitations
with respect to large-scale ones. This exponent yields the standard thermal
exponent of droplet theory theta through the relation, theta=d(lambda-1). Our
work provides a new way to measure the thermal exponent theta without any
assumption about the procedure to generate typical low-lying excitations. We
find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal
exponent obtained in domain-wall theory showing that MacMillan excitations are
not typical.Comment: 4 pages, 3 figures, (v2) revised version, (v3) corrected typo
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