21 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
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
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
Hysteresis loop signatures of phase transitions in a mean-field model of disordered Ising magnet
In accordance with recent experiments the mean-field type theories predict
the presence of numerous metastable minima (states) in the rugged free-energy
landscape of frustrated disordered magnets. This multiplicity of long-lived
states with lifetimes greater than makes the task to experimentally
determine which of them has the lowest free energy (and thus what thermodynamic
phase the sample is in) seem rather hopeless the more so as we do not know a
protocol (such as field-cooling or zero-field-cooling) leading to the
equilibrium state(s). Nevertheless here we show in the framework of Landau-type
phenomenological model that signatures of the mean-field equilibrium phase
transitions in such highly nonequilibrium systems may be found in the evolution
of the hysteresis loop form. Thus the sequence of transitions from spin-glass
to mixed phase and to ferromagnetic one results in the changes from inclined
hysteresis loop to that with the developing vertical sides and to one with the
perfectly vertical sides. Such relation between loop form and the location of
global minimum may hold beyond the mean-field approximation and can be useful
in the real experiments and Monte-Carlo simulations of the problems involving
rugged potential landscape. Also the very existence of the quasi-static loops
in spin glass and mixed phases implies that the known disorder-smoothing of the
first-order transition can be always accompanied by the emergence of multiple
metastable states.Comment: 5 pages, 4 figures; misprints corrected, slight deviations from
published version (abstract and references
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
Spatially heterogeneous ages in glassy dynamics
We construct a framework for the study of fluctuations in the nonequilibrium
relaxation of glassy systems with and without quenched disorder. We study two
types of two-time local correlators with the aim of characterizing the
heterogeneous evolution: in one case we average the local correlators over
histories of the thermal noise, in the other case we simply coarse-grain the
local correlators. We explain why the former describe the fingerprint of
quenched disorder when it exists, while the latter are linked to noise-induced
mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations
of the coarse-grained quantities. We show that locally defined correlations and
responses are connected by a generalized local out-of-equilibrium
fluctuation-dissipation relation. We argue that large-size heterogeneities in
the age of the system survive in the long-time limit. The invariance of the
theory under reparametrizations of time underlies these results. We relate the
pdfs of local coarse-grained quantities and the theory of dynamic random
manifolds. We define a two-time dependent correlation length from the spatial
decay of the fluctuations in the two-time local functions. We present numerical
tests performed on disordered spin models in finite and infinite dimensions.
Finally, we explain how these ideas can be applied to the analysis of the
dynamics of other glassy systems that can be either spin models without
disorder or atomic and molecular glassy systems.Comment: 47 pages, 60 Fig