378 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
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
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
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
Canonical solution of a system of long-range interacting rotators on a lattice
The canonical partition function of a system of rotators (classical X-Y
spins) on a lattice, coupled by terms decaying as the inverse of their distance
to the power alpha, is analytically computed. It is also shown how to compute a
rescaling function that allows to reduce the model, for any d-dimensional
lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees'
Comments it has been transferred to Phys. Rev. E, because of supposed no
general interest. Divided into sections, corrections in (5) and (20),
reference 5 updated. 8 pages 1 figur
Implanted muon spin spectroscopy on 2-O-adamantane: a model system that mimics the liquid
The transition taking place between two metastable phases in 2-O-adamantane, namely the [Formula: see text] cubic, rotator phase and the lower temperature P21/c, Z = 4 substitutionally disordered crystal is studied by means of muon spin rotation and relaxation techniques. Measurements carried out under zero, weak transverse and longitudinal fields reveal a temperature dependence of the relaxation parameters strikingly similar to those exhibited by structural glass[Formula: see text]liquid transitions (Bermejo et al 2004 Phys. Rev. B 70 214202; Cabrillo et al 2003 Phys. Rev. B 67 184201). The observed behaviour manifests itself as a square root singularity in the relaxation rates pointing towards some critical temperature which for amorphous systems is located some tens of degrees above that shown as the characteristic transition temperature if studied by thermodynamic means. The implications of such findings in the context of current theoretical approaches concerning the canonical liquid-glass transition are discussed.Postprint (author's final draft
Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups
We consider noncommutative GUT inspired field theories formulated within the
enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our
theories have only gauge fields and fermions, and we compute the UV divergent
part of the one-loop background-field effective action involving two fermionic
fields at first order in the noncommutativity parameter theta. We show that, if
the second-degree Casimir has the same value for all the irreps furnished by
the fermionic multiplets of the model, then, that UV divergent part can be
renormalised by carrying out multiplicative renormalisations of the coupling
constant, theta and the fields, along with the inclusion of theta-dependent
counterterms which vanish upon imposing the equations of motion. These
theta-dependent counterterms have no physical effect since they vanish
on-shell. This result along with the vanishing of the UV divergent part of the
fermionic four-point functions leads to the unexpected conclusion that the
one-loop matter sector of the background-field effective action of these
theories is one-loop multiplicatively renormalisable on-shell. We also show
that the background-field effective action of the gauge sector of the theories
considered here receives no theta-dependent UV divergent contributions at
one-loop. We thus conclude that these theories are on-shell one-loop
multiplicatively renormalisable at first order in theta.Comment: 20 pages, 3 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
Disentangling α and β relaxation in orientationally disordered crystals with theory and experiments.
We use a microscopically motivated generalized Langevin equation (GLE) approach to link the vibrational density of states (VDOS) to the dielectric response of orientational glasses (OGs). The dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of two OGs: freon-112 and freon-113, around and just above T_{g}. The memory function is related to the integral of the VDOS times a spectral coupling function γ(ω_{p}), which tells the degree of dynamical coupling between molecular degrees of freedom at different eigenfrequencies. The comparative analysis of the two freons reveals that the appearance of a secondary β relaxation in freon-112 is due to cooperative dynamical coupling in the regime of mesoscopic motions caused by stronger anharmonicity (absent in freon-113) and is associated with the comparatively lower boson peak in the VDOS. The proposed framework brings together all the key aspects of glassy physics (VDOS with the boson peak, dynamical heterogeneity, dissipation, and anharmonicity) into a single model
- …