6,059 research outputs found
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
Thermal Model Calibration for Minor Planets Observed with Wide-Field Infrared Survey Explorer/Neowise
With the Wide-field Infrared Survey Explorer (WISE), we have observed over 157,000 minor planets. Included in these are a number of near-Earth objects, main-belt asteroids, and irregular satellites which have well measured physical properties (via radar studies and in situ imaging) such as diameters. We have used these objects to validate models of thermal emission and reflected sunlight using the WISE measurements, as well as the color corrections derived in Wright et al. for the four WISE bandpasses as a function of effective temperature. We have used 50 objects with diameters measured by radar or in situ imaging to characterize the systematic errors implicit in using the WISE data with a faceted spherical near-Earth asteroid thermal model (NEATM) to compute diameters and albedos. By using the previously measured diameters and H magnitudes with a spherical NEATM model, we compute the predicted fluxes (after applying the color corrections given in Wright et al.) in each of the four WISE bands and compare them to the measured magnitudes. We find minimum systematic flux errors of 5%-10%, and hence minimum relative diameter and albedo errors of ~10% and ~20%, respectively. Additionally, visible albedos for the objects are computed and compared to the albedos at 3.4 μm and 4.6 μm, which contain a combination of reflected sunlight and thermal emission for most minor planets observed by WISE. Finally, we derive a linear relationship between subsolar temperature and effective temperature, which allows the color corrections given in Wright et al. to be used for minor planets by computing only subsolar temperature instead of a faceted thermophysical model. The thermal models derived in this paper are not intended to supplant previous measurements made using radar or spacecraft imaging; rather, we have used them to characterize the errors that should be expected when computing diameters and albedos of minor planets observed by WISE using a spherical NEATM model
Numerical Study of Order in a Gauge Glass Model
The XY model with quenched random phase shifts is studied by a T=0 finite
size defect energy scaling method in 2d and 3d. The defect energy is defined by
a change in the boundary conditions from those compatible with the true ground
state configuration for a given realization of disorder. A numerical technique,
which is exact in principle, is used to evaluate this energy and to estimate
the stiffness exponent . This method gives in
2d and in 3d, which are considerably larger than
previous estimates, strongly suggesting that the lower critical dimension is
less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let
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
Abstract Interpretation with Unfoldings
We present and evaluate a technique for computing path-sensitive interference
conditions during abstract interpretation of concurrent programs. In lieu of
fixed point computation, we use prime event structures to compactly represent
causal dependence and interference between sequences of transformers. Our main
contribution is an unfolding algorithm that uses a new notion of independence
to avoid redundant transformer application, thread-local fixed points to reduce
the size of the unfolding, and a novel cutoff criterion based on subsumption to
guarantee termination of the analysis. Our experiments show that the abstract
unfolding produces an order of magnitude fewer false alarms than a mature
abstract interpreter, while being several orders of magnitude faster than
solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to
appear at CAV 201
Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass
We study how the ground state of the two-dimensional Ising spin glass with
Gaussian interactions in zero magnetic field changes on altering the boundary
conditions. The probability that relative spin orientations change in a region
far from the boundary goes to zero with the (linear) size of the system L like
L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to
d-d_f where d (=2) is the dimension of the system and d_f is the fractal
dimension of a domain wall induced by changes in the boundary conditions. Our
value for d_f is consistent with earlier estimates. These results show that, at
zero temperature, there is only a single pure state (plus the state with all
spins flipped) in agreement with the predictions of the droplet model.Comment: 4 pages, 3 postscript figures; some changes in response to referees'
comments, to appear in Phys Rev. B, Rapid Communications, Oct.
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