59 research outputs found
Non-compact local excitations in spin glasses
We study numerically the local low-energy excitations in the 3-d
Edwards-Anderson model for spin glasses. Given the ground state, we determine
the lowest-lying connected cluster of flipped spins with a fixed volume
containing one given spin. These excitations are not compact, having a fractal
dimension close to two, suggesting an analogy with lattice animals. Also, their
energy does not grow with their size; the associated exponent is slightly
negative whereas the one for compact clusters is positive. These findings call
for a modification of the basic hypotheses underlying the droplet model.Comment: 7 pages, LaTex, discussion on stability clarifie
Energetics of clusters in the two-dimensional Ising spin glass
We study numerically the properties of local low-energy excitations in the
two-dimensional Ising spin glass. Given the ground state, we determine the
lowest-lying connected cluster of flipped spins containing one given spin,
either with a fixed volume, or with a volume constrained to lie in a certain
range. Our aim is to understand corrections to the scaling predicted by the
droplet picture of spin glasses and to resolve contradictory results reported
in the literature for the stiffness exponent. We find no clear trace of
corrections to scaling, and the obtained stiffness exponent is in relatively
good agreement with standard domain wall calculations.Comment: 8 pages, 9 figure
Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets
Using the functional renormalization group (FRG) we study the thermal
fluctuations of elastic objects, described by a displacement field u and
internal dimension d, pinned by a random potential at low temperature T, as
prototypes for glasses. A challenge is how the field theory can describe both
typical (minimum energy T=0) configurations, as well as thermal averages which,
at any non-zero T as in the phenomenological droplet picture, are dominated by
rare degeneracies between low lying minima. We show that this occurs through an
essentially non-perturbative *thermal boundary layer* (TBL) in the (running)
effective action Gamma[u] at T>0 for which we find a consistent scaling ansatz
to all orders. The TBL resolves the singularities of the T=0 theory and
contains rare droplet physics. The formal structure of this TBL is explored
around d=4 using a one loop Wilson RG. A more systematic Exact RG (ERG) method
is employed and tested on d=0 models. There we obtain precise relations between
TBL quantities and droplet probabilities which are checked against exact
results. We illustrate how the TBL scaling remains consistent to all orders in
higher d using the ERG and how droplet picture results can be retrieved.
Finally, we solve for d=0,N=1 the formidable "matching problem" of how this T>0
TBL recovers a critical T=0 field theory. We thereby obtain the beta-function
at T=0, *all ambiguities removed*, displayed here up to four loops. A
discussion of d>4 case and an exact solution at large d are also provided
Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
The energy of a droplet of linear extent l in the droplet theory of spin
glasses goes as l^{\theta} for large l. It is shown by numerical studies of
large droplets in two-dimensional systems that this formula needs to be
modified by the addition of a scaling correction l^{-\omega} in order to
accurately describe droplet energies at the length scales currently probed in
numerical simulations. Using this simple modification it is now possible to
explain many results with the droplet model which have been found in
simulations of three-dimensional Ising spin glasses.Comment: 4 pages, 2 figures, revte
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Dynamic scaling and aging phenomena in short-range Ising spin glass: CuCoCl-FeCl graphite bi-intercalation compound
Static and dynamic behavior of short-range Ising-spin glass
CuCoCl-FeCl graphite bi-intercalation compounds
(GBIC) has been studied with SQUID DC and AC magnetic susceptibility. The
dependence of the zero-field relaxation time above a spin-freezing
temperature (= 3.92 0.11 K) is well described by critical slowing
down. The absorption below decreases with
increasing angular frequency , which is in contrast to the case of 3D
Ising spin glass. The dynamic freezing temperature at which
dd, is determined as a function of
frequency (0.01 Hz 1 kHz) and magnetic field (0 5 kOe). The dynamic scaling analysis of the relaxation time
defined as at suggests the absence of
SG phase in the presence of (at least above 100 Oe). Dynamic scaling
analysis of and near
leads to the critical exponents ( = 0.36 0.03, = 3.5
0.4, = 1.4 0.2, = 6.6 1.2, = 0.24
0.02, and = 0.13 0.02). The aging phenomenon is studied through
the absorption below . It obeys a
power-law decay with an exponent . The rejuvenation effect is also observed under
sufficiently large (temperature and magnetic-field) perturbations.Comment: 14 pages, 19 figures; to be published in Phys. Rev. B (September 1,
2003
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
Evidence for the double degeneracy of the ground-state in the 3D spin glass
A bivariate version of the multicanonical Monte Carlo method and its
application to the simulation of the three-dimensional Ising spin glass
are described. We found the autocorrelation time associated with this
particular multicanonical method was approximately proportional to the system
volume, which is a great improvement over previous methods applied to
spin-glass simulations. The principal advantage of this version of the
multicanonical method, however, was its ability to access information
predictive of low-temperature behavior. At low temperatures we found results on
the three-dimensional Ising spin glass consistent with a double
degeneracy of the ground-state: the order-parameter distribution function
converged to two delta-function peaks and the Binder parameter
approached unity as the system size was increased. With the same density of
states used to compute these properties at low temperature, we found their
behavior changing as the temperature is increased towards the spin glass
transition temperature. Just below this temperature, the behavior is consistent
with the standard mean-field picture that has an infinitely degenerate ground
state. Using the concept of zero-energy droplets, we also discuss the structure
of the ground-state degeneracy. The size distribution of the zero-energy
droplets was found to produce the two delta-function peaks of .Comment: 33 pages with 31 eps figures include
Real spin glasses relax slowly in the shade of hierarchical trees
The Parisi solution of the mean-field spin glass has been widely accepted and
celebrated. Its marginal stability in 3d and its complexity however raised the
question of its relevance to real spin glasses. This paper gives a short
overview of the important experimental results which could be understood within
the mean-field solution. The existence of a true phase transition and the
particular behaviour of the susceptibility below the freezing temperature,
predicted by the theory, are clearly confirmed by the experimental results. The
behaviour of the complex order parameter and of the Fluctuation Dissipation
ratio are in good agreement with results of spontaneous noise measurements. The
very particular ultrametric symmetry, the key feature of the theory, provided
us with a simple description of the rejuvenation and memory effects observed in
experiment. Finally, going a step beyond mean-field, the paper shortly
discusses new analyses in terms of correlated domains characterized by their
length scales, as well as new experiments on superspin glasses which compare
well with recent theoretical simulations.Comment: To appear in the proceedings of "Wandering with Curiosity in Complex
Landscapes", a scientific conference in honour of Giorgio Parisi for his 60th
birthday, Roma, September 8-10 2008 (submitted for the special issue of the
Journal of Statistical Physics, 2009
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