277 research outputs found
Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices
Using Grassmann variables and an analogy with two dimensional electrostatics,
we obtain the average eigenvalue distribution of ensembles of asymmetrically diluted Hopfield matrices in the limit . We found that in the limit of strong dilution the distribution is
uniform in a circle in the complex plane.Comment: 9 pages, latex, 4 figure
Aging dynamics of +-J Edwards-Anderson spin glasses
We analyze by means of extensive computer simulations the out of equilibrium
dynamics of Edwards-Anderson spin glasses in d=4 and d=6 dimensions with +-J
interactions. In particular, we focus our analysis on the scaling properties of
the two-time autocorrelation function in a range of temperatures from T=0.07
T_c to T=0.75 T_c in both systems. We observe that the aging dynamics of the
+-J models is different from that observed in the corresponding Gaussian
models. In both the 4d and 6d models at very low temperatures we study the
effects of discretization of energy levels. Strong interrupted aging behaviors
are found. We argue that this is because in the times accessible to our
simulations the systems are only able to probe activated dynamics through the
lowest discrete energy levels and remain trapped around nearly flat regions of
the energy landscape. For temperatures T >= 0.5 T_c in 4d we find logarithmic
scalings that are compatible with dynamical ultrametricity, while in 6d the
relaxation can also be described by super-aging scalings.Comment: 7 pages, 10 figure
Influence of Refractory Periods in the Hopfield model
We study both analytically and numerically the effects of including
refractory periods in the Hopfield model for associative memory. These periods
are introduced in the dynamics of the network as thresholds that depend on the
state of the neuron at the previous time. Both the retrieval properties and the
dynamical behaviour are analyzed.Comment: Revtex, 7 pages, 7 figure
The exchange bias phenomenon in uncompensated interfaces: Theory and Monte Carlo simulations
We performed Monte Carlo simulations in a bilayer system composed by two thin
films, one ferromagnetic (FM) and the other antiferromagnetic (AFM). Two
lattice structures for the films were considered: simple cubic (sc) and a body
center cubic (bcc). In both lattices structures we imposed an uncompensated
interfacial spin structure, in particular we emulated a FeF2-FM system in the
case of the (bcc) lattice. Our analysis focused on the incidence of the
interfacial strength interactions between the films J_eb and the effect of
thermal fluctuations on the bias field H_EB. We first performed Monte Carlo
simulations on a microscopic model based on classical Heisenberg spin
variables. To analyze the simulation results we also introduced a simplified
model that assumes coherent rotation of spins located on the same layer
parallel to the interface. We found that, depending on the AFM film anisotropy
to exchange ratio, the bias field is either controlled by the intrinsic pinning
of a domain wall parallel to the interface or by the stability of the first AFM
layer (quasi domain wall) near the interface.Comment: 18 pages, 11 figure
Long-range effects in granular avalanching
We introduce a model for granular flow in a one-dimensional rice pile that
incorporates rolling effects through a long-range rolling probability for the
individual rice grains proportional to , being the distance
traveled by a grain in a single topling event. The exponent controls the
average rolling distance. We have shown that the crossover from power law to
stretched exponential behaviors observed experimentally in the granular
dynamics of rice piles can be well described as a long-range effect resulting
from a change in the transport properties of individual grains. We showed that
stretched exponential avalanche distributions can be associated with a
long-range regime for where the average rolling distance grows as a
power law with the system size, while power law distributions are associated
with a short range regime for , where the average rolling distance is
independent of the system size.Comment: 5 pages, 3 figure
Aging in an infinite-range Hamiltonian system of coupled rotators
We analyze numerically the out-of-equilibrium relaxation dynamics of a
long-range Hamiltonian system of fully coupled rotators. For a particular
family of initial conditions, this system is known to enter a particular regime
in which the dynamic behavior does not agree with thermodynamic predictions.
Moreover, there is evidence that in the thermodynamic limit, when
is taken prior to , the system will never attain true equilibrium.
By analyzing the scaling properties of the two-time autocorrelation function we
find that, in that regime, a very complex dynamics unfolds in which {\em aging}
phenomena appear. The scaling law strongly suggests that the system behaves in
a complex way, relaxing towards equilibrium through intricate trajectories. The
present results are obtained for conservative dynamics, where there is no
thermal bath in contact with the system. This is the first time that aging is
observed in such Hamiltonian systems.Comment: Figs. 2-4 modified, minor changes in text. To appear in Phys. Rev.
Damage spreading in random field systems
We investigate how a quenched random field influences the damage spreading
transition in kinetic Ising models. To this end we generalize a recent master
equation approach and derive an effective field theory for damage spreading in
random field systems. This theory is applied to the Glauber Ising model with a
bimodal random field distribution. We find that the random field influences the
spreading transition by two different mechanisms with opposite effects. First,
the random field favors the same particular direction of the spin variable at
each site in both systems which reduces the damage. Second, the random field
suppresses the magnetization which, in turn, tends to increase the damage. The
competition between these two effects leads to a rich behavior.Comment: 4 pages RevTeX, 3 eps figure
Linear instability and statistical laws of physics
We show that a meaningful statistical description is possible in conservative
and mixing systems with zero Lyapunov exponent in which the dynamical
instability is only linear in time. More specifically, (i) the sensitivity to
initial conditions is given by with
; (ii) the statistical entropy in the infinitely fine graining limit (i.e., {\it
number of cells into which the phase space has been partitioned} ),
increases linearly with time only for ; (iii) a nontrivial,
-generalized, Pesin-like identity is satisfied, namely the . These facts (which are
in analogy to the usual behaviour of strongly chaotic systems with ), seem
to open the door for a statistical description of conservative many-body
nonlinear systems whose Lyapunov spectrum vanishes.Comment: 7 pages including 2 figures. The present version is accepted for
publication in Europhysics Letter
Interplay between coarsening and nucleation in an Ising model with dipolar interactions
We study the dynamical behavior of a square lattice Ising model with exchange
and dipolar interactions by means of Monte Carlo simulations. After a sudden
quench to low temperatures we find that the system may undergo a coarsening
process where stripe phases with different orientations compete or
alternatively it can relax initially to a metastable nematic phase and then
decay to the equilibrium stripe phase through nucleation. We measure the
distribution of equilibration times for both processes and compute their
relative probability of occurrence as a function of temperature and system
size. This peculiar relaxation mechanism is due to the strong metastability of
the nematic phase, which goes deep in the low temperature stripe phase. We also
measure quasi-equilibrium autocorrelations in a wide range of temperatures.
They show a distinct decay to a plateau that we identify as due to a finite
fraction of frozen spins in the nematic phase. We find indications that the
plateau is a finite size effect. Relaxation times as a function of temperature
in the metastable region show super-Arrhenius behavior, suggesting a possible
glassy behavior of the system at low temperatures
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