204 research outputs found
Energetics and geometry of excitations in random systems
Methods for studying droplets in models with quenched disorder are critically
examined. Low energy excitations in two dimensional models are investigated by
finding minimal energy interior excitations and by computing the effect of bulk
perturbations. The numerical data support the assumptions of compact droplets
and a single exponent for droplet energy scaling. Analytic calculations show
how strong corrections to power laws can result when samples and droplets are
averaged over. Such corrections can explain apparent discrepancies in several
previous numerical results for spin glasses.Comment: 4 pages, eps files include
Field-Shift Aging Protocol on the 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and Paramagnetic States
Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model
under a static magnetic field are examined by means of the standard Monte
Carlo simulation on the field-shift aging protocol at temperature . For each
process with (T; \tw, h), \tw being the waiting time before the field is
switched on, we extract the dynamical crossover time, \tcr(T; \tw, h). We
have found a nice scaling relation between the two characteristic length scales
which are properly determined from \tcr and \tw and then are normalized by
the static field crossover length introduced in the SG droplet theory. This
scaling behavior implies the instability of the SG phase in the equilibrium
limit even under an infinitesimal . In comparison with this numerical result
the field effect on real spin glasses is also discussed.Comment: 4 pages, 5 figures, jpsj2, Changed conten
Energy landscapes in random systems, driven interfaces and wetting
We discuss the zero-temperature susceptibility of elastic manifolds with
quenched randomness. It diverges with system size due to low-lying local
minima. The distribution of energy gaps is deduced to be constant in the limit
of vanishing gaps by comparing numerics with a probabilistic argument. The
typical manifold response arises from a level-crossing phenomenon and implies
that wetting in random systems begins with a discrete transition. The
associated ``jump field'' scales as and for
(1+1) and (2+1) dimensional manifolds with random bond disorder.Comment: Accepted for publication in Phys. Rev. Let
Real space application of the mean-field description of spin glass dynamics
The out of equilibrium dynamics of finite dimensional spin glasses is
considered from a point of view going beyond the standard `mean-field theory'
versus `droplet picture' debate of the last decades. The main predictions of
both theories concerning the spin glass dynamics are discussed. It is shown, in
particular, that predictions originating from mean-field ideas concerning the
violations of the fluctuation-dissipation theorem apply quantitatively,
provided one properly takes into account the role of the spin glass coherence
length which plays a central role in the droplet picture. Dynamics in a uniform
magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio
Spin glass transition in a magnetic field: a renormalization group study
We study the transition of short range Ising spin glasses in a magnetic
field, within a general replica symmetric field theory, which contains three
masses and eight cubic couplings, that is defined in terms of the fields
representing the replicon, anomalous and longitudinal modes. We discuss the
symmetry of the theory in the limit of replica number n to 0, and consider the
regular case where the longitudinal and anomalous masses remain degenerate.
The spin glass transitions in zero and non-zero field are analyzed in a
common framework. The mean field treatment shows the usual results, that is a
transition in zero field, where all the modes become critical, and a transition
in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon
mode critical. Renormalization group methods are used to study the critical
behavior, to order epsilon = 6-d. In the general theory we find a stable
fixed-point associated to the spin glass transition in zero field. This
fixed-point becomes unstable in the presence of a small magnetic field, and we
calculate crossover exponents, which we relate to zero-field critical
exponents. In a finite magnetic field, we find no physical stable fixed-point
to describe the AT transition, in agreement with previous results of other
authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.
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
No spin-glass transition in the "mobile-bond" model
The recently introduced ``mobile-bond'' model for two-dimensional spin
glasses is studied. The model is characterized by an annealing temperature T_q.
On the basis of Monte Carlo simulations of small systems it has been claimed
that this model exhibits a non-trivial spin-glass transition at finite
temperature for small values of T_q.
Here the model is studied by means of exact ground-state calculations of
large systems up to N=256^2. The scaling of domain-wall energies is
investigated as a function of the system size. For small values T_q<0.95 the
system behaves like a (gauge-transformed) ferromagnet having a small fraction
of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard
two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at
T>0.Comment: 4 pages, 5 figures, RevTe
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
Ground states of two-dimensional J Edwards-Anderson spin glasses
We present an exact algorithm for finding all the ground states of the
two-dimensional Edwards-Anderson spin glass and characterize its
performance. We investigate how the ground states change with increasing system
size and and with increasing antiferromagnetic bond ratio . We find that
that some system properties have very large and strongly non-Gaussian
variations between realizations.Comment: 15 pages, 21 figures, 2 tables, uses revtex4 macro
Extremal Optimization of Graph Partitioning at the Percolation Threshold
The benefits of a recently proposed method to approximate hard optimization
problems are demonstrated on the graph partitioning problem. The performance of
this new method, called Extremal Optimization, is compared to Simulated
Annealing in extensive numerical simulations. While generally a complex
(NP-hard) problem, the optimization of the graph partitions is particularly
difficult for sparse graphs with average connectivities near the percolation
threshold. At this threshold, the relative error of Simulated Annealing for
large graphs is found to diverge relative to Extremal Optimization at equalized
runtime. On the other hand, Extremal Optimization, based on the extremal
dynamics of self-organized critical systems, reproduces known results about
optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of
Physics
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