546 research outputs found
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
Disorder-induced mechanism for positive exchange bias fields
We propose a mechanism to explain the phenomenon of positive exchange bias on
magnetic bilayered systems. The mechanism is based on the formation of a domain
wall at a disordered interface during field cooling (FC) which induces a
symmetry breaking of the antiferromagnet, without relying on any ad hoc
assumption about the coupling between the ferromagnetic (FM) and
antiferromagnetic (AFM) layers. The domain wall is a result of the disorder at
the interface between FM and AFM, which reduces the effective anisotropy in the
region. We show that the proposed mechanism explains several known experimental
facts within a single theoretical framework. This result is supported by Monte
Carlo simulations on a microscopic Heisenberg model, by micromagnetic
calculations at zero temperature and by mean field analysis of an effective
Ising like phenomenological model.Comment: 5 pages, 4 figure
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
On the length and area spectrum of analytic convex domains
Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second,
we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.Peer ReviewedPostprint (author's final draft
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
Stability as a natural selection mechanism on interacting networks
Biological networks of interacting agents exhibit similar topological
properties for a wide range of scales, from cellular to ecological levels,
suggesting the existence of a common evolutionary origin. A general
evolutionary mechanism based on global stability has been proposed recently [J
I Perotti, O V Billoni, F A Tamarit, D R Chialvo, S A Cannas, Phys. Rev. Lett.
103, 108701 (2009)]. This mechanism is incorporated into a model of a growing
network of interacting agents in which each new agent's membership in the
network is determined by the agent's effect on the network's global stability.
We show that, out of this stability constraint, several topological properties
observed in biological networks emerge in a self organized manner. The
influence of the stability selection mechanism on the dynamics associated to
the resulting network is analyzed as well.Comment: 10 pages, 9 figure
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