Papers by Daniel Stariolo
Physical Review B, May 18, 2006
Network: Computation In Neural Systems, 1996
A Tsallis-statistics-based generalization of the gradient descent dynamics (using nonextensive co... more A Tsallis-statistics-based generalization of the gradient descent dynamics (using nonextensive cost functions), recently introduced by one of us, is proposed as a learning rule in a simple perceptron. The resulting Langevin equations are solved numerically for different values of an index q (q = 1 and q = 1 respectively correspond to the extensive and non-extensive cases) and for different cost functions. The results are compared with the learning curve (mean error versus time) obtained from a learning experiment carried out with human beings, showing an excellent agreement for values of q slightly above unity. This fact illustrates the possible importance of including some degree of non-locality (non-extensivity) in computational learning procedures, whenever one wants to mimic human behaviour.
Physical Review Letters, Nov 30, 2007
Physical Review B, Aug 31, 2007
We show results from simulations of the Langevin dynamics of a two-dimensional scalar model with ... more We show results from simulations of the Langevin dynamics of a two-dimensional scalar model with competing interactions for ultrathin magnetic films. We find a phase transition from a high temperature disordered phase to a low temperature phase with both translational and orientational orders. Both kinds of order emerge at the same temperature, probably due to the isotropy of the model Hamiltonian. In the low temperature phase orientational correlations show long range order while translational ones show only quasi-long-range order in a wide temperature range. The orientational correlation length and the associated susceptibility seem to diverge with power laws at the transition. While at zero temperature the system exhibits stripe long range order, as temperature grows we observe the proliferation of different kinds of topological defects that ultimately drive the system to the disordered phase. The magnetic structures observed are similar to experimental results on ultrathin ferromagnetic films.
Physica D: Nonlinear Phenomena, May 1, 2001
We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions ... more We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r −(d+σ). The long time dynamics of correlations and responses are studied in detail in the different dynamical regimes and the validity of fluctuation-dissipation relations (or its violation) are shown. In particular, we show that the fluctuation-dissipation ratio X(t + tw, tw) is assymptotically a fucntion only of the waiting time tw in the aging regime and that X → 0 as tw → ∞. The results are valid in any finite dimension d and for 0 < σ < 2 where short range behavior is recovered. We also solve the T = 0 Cahn-Hilliard dynamics of this model (conserved order parameter). An analysis of the multiscaling behavior of the autocorrelation function is presented.
arXiv (Cornell University), Dec 15, 2021
The size and shape of the region affected by an outbreak is relevant to understand the dynamics o... more The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents diffuse on a regular lattice and the disease may be transmitted when an infected and a susceptible agents are nearest neighbors. We study the geometric properties of both the connected cluster of sites visited by infected agents (outbreak cluster) and the set of clusters with sites that have not been visited. By changing the density of agents, our results show that there is a mixed-order (hybrid) transition where the region affected by the disease is finite in one phase but percolates through the system beyond the threshold. Moreover, the outbreak cluster seems to have the same exponents of the backbone of the critical cluster of the ordinary percolation while the clusters with unvisited sites have a size distribution with a Fisher exponent τ < 2.
Langevin simulations of two dimensional systems with competing interactions
Optimal Hebbian Learning Rules and the Role of Asymmetry
International Journal of Neural Systems, Jun 1, 1994
We study the storage properties associated with generalized Hebbian learning rules which present ... more We study the storage properties associated with generalized Hebbian learning rules which present four free parameters that allow for asymmetry. We also introduce two extra parameters in the post-synaptic potentials in order to further improve the critical capacity. Using signal-to-noise analysis, as well as computer simulations on an analog network, we discuss the performance of the rules for arbitrarily biased patterns and find that the critical storage capacity alpha c becomes maximal for a particular symmetric rule (alpha c diverges in the sparse coding limit). Departures from symmetry decrease alpha c but can increase the robustness of the model.
Orientational order in systems with competing interactions
Journal of physics, Sep 1, 2010
Physical review, Aug 17, 2020
We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising p-sp... more We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising p-spin Model with p = 3 and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers and trapping times on subsequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various Trap Models finding the best agreement with the Step Model when the p-spin configurations are constrained to be uncorrelated.
Optimization by Simulated Annealing: Recent Progress
WORLD SCIENTIFIC eBooks, Mar 1, 1995
Physical Review B, Jul 18, 2011
We show that the mean field phase diagram of the dipolar frustrated ferromagnet in an external fi... more We show that the mean field phase diagram of the dipolar frustrated ferromagnet in an external field presents an inverse transition in the field-temperature plane. The presence of this type of transition has recently been observed experimentally in ultrathin films of Fe/Cu(001). We study a coarse-grained model Hamiltonian in two dimensions. The model supports stripe and bubble equilibrium phases, as well as the paramagnetic phase. At variance with common expectations, already in a single mode approximation, the model shows a sequence of paramagnetic-bubblesstripes-paramagnetic phase transitions upon lowering the temperature at fixed external field. Going beyond the single mode approximation leads to the shrinking of the bubbles phase, which is restricted to a small region near the zero field critical temperature. Monte Carlo simulations results with a Heisenberg model are consistent with the mean field results.
Finite-size relaxational dynamics of a spike random matrix spherical model
arXiv (Cornell University), May 31, 2023
arXiv (Cornell University), May 19, 2009
We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic... more We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic films. The model is based on the interaction between dipolar as well as quadrupolar magnetic moments. In the special case of strong perpendicular crystal anisotropy, we show that quadrupolar degrees of freedom associated with orientation of domain walls are essential in order to correctly describe the observed phenomenology of domain formation. A nematic phase characterized by orientational order of domain walls (stripe-like) but without translational order is predicted. This isotropic-nematic transition belongs to the Kosterlitz-Thouless type in the thermodynamic limit. However, we found that in actual experimental scales, the fluctuations of the nematic order parameter are regularized by the sample size, and orientational long range order, as predicted by mean field, should be observable. The transition may be completely characterized experimentally from measurements of the magnetic structure factor as well as from the non-linear in-plane magnetic susceptibility.
arXiv (Cornell University), Sep 23, 2005
Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by mol... more Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. The van Hove distribution of particle displacements and the self part of the incoherent scattering function on a large window of time and length scales are measured in order to characterize particle diffusion. We consider inherent structures dynamics in order to filter out vibrational motion. We find at least three clear regimes in both functions: a persistence dominated regime at short times and small length scales, a strongly correlated regime of particle motion at intermediate time-lengths and a Gaussian or Fickian asymptotic regime at long times/lengths. The crossovers between these regimes allow us to obtain two characteristic length scales from two point functions. The functional forms of the observables and time/length scalings are considered. A comparison with available experimental results on local particle motion is done.
Physical review, Aug 1, 1999
The violation of the Fluctuation-Dissipation Theorem (FDT) in a two-dimensional Ising model with ... more The violation of the Fluctuation-Dissipation Theorem (FDT) in a two-dimensional Ising model with both ferromagnetic exchange and antiferromagnetic dipolar interactions is established and investigated via Monte Carlo simulations. Through the computation of the autocorrelation C(t + tw, tw) and the integrated response (susceptibility) functions we obtain the F DT violation factor X(t+tw, tw) for different values of the temperature, the waiting time tw and the quotient δ = J0/J d , J0 and J d being the strength of exchange and dipolar interactions respectively. For positive values of δ this system develops a striped phase at low temperatures, in which the non-equilibrium dynamics presents two different regimes. Our results show that such different regimes are not reflected in the F DT violation factor, where X goes always to zero for high values of tw in the aging regime, a result that appears in domain growth processes in non-frustrated ordered systems.
Physical Review B, Apr 7, 2008
We show results from Monte Carlo simulations of a two-dimensional Heisenberg model for ultrathin ... more We show results from Monte Carlo simulations of a two-dimensional Heisenberg model for ultrathin films with perpendicular anisotropy. A complete phase diagram is obtained as a function of anisotropy and temperature, spanning a wide range of behavior. We discuss our results in relation to experimental findings in different ultrathin films. We observe and characterize a line of spin reorientation transitions. This transition from out-of-plane stripe order to in-plane ferromagnetic order presents an intermediate paramagnetic gap in a finite region of parameter space, as reported in experiments. For large anisotropies, direct transitions from a low temperature stripe phase to a paramagnetic or tetragonal phase with dominant perpendicular magnetization is observed, which is also in agreement with experiments. We also show the phase diagram for a system without exchange, i.e., with pure dipolar and anisotropy interactions. It shows a similar behavior to the ferromagnetic case with antiferromagnetic instead of stripe phases at low temperatures. A spin reorientation transition is also found in this case.
Journal of Magnetism and Magnetic Materials, Dec 1, 2010
We present the complete zero temperature phase diagram of a model for ultrathin films with perpen... more We present the complete zero temperature phase diagram of a model for ultrathin films with perpendicular anisotropy. The whole parameter space of relevant coupling constants is studied in first order anisotropy approximation. Because the ground state is known to be formed by perpendicular stripes separated by Bloch walls, a standard variational approach is used, complemented with specially designed Monte Carlo simulations. We can distinguish four regimes according to the different nature of striped domains: a high anisotropy Ising regime with sharp domain walls, a saturated stripe regime with thicker walls inside which an in-plane component of the magnetization develops, a narrow canted-like regime, characterized by a sinusoidal variation of both the in-plane and the out of plane magnetization components, which upon further decrease of the anisotropy leads to an in-plane ferromagnetic state via a spin reorientation transition (SRT). The nature of domains and walls are described in some detail together with the variation of domain width with anisotropy, for any value of exchange and dipolar interactions. Our results, although strictly valid at T = 0, can be valuable for interpreting data on the evolution of domain width at finite temperature, a still largely open problem.
Ising spin glasses with multispin interactions
Physica D: Nonlinear Phenomena, Jul 1, 1990
ABSTRACT We study the phase structure of Ising spin glass models with interactions between 3, 5 a... more ABSTRACT We study the phase structure of Ising spin glass models with interactions between 3, 5 and 10 spins in the Hamiltonian. We used the replica mean field theory approach and solved numerically the saddle point equations. We found evidence of three phases: a disordered phase and two spin glass phases at low temperatures. Present address: Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Xavier Sigaud 150, 22290 Rio de Janeiro, RJ, Brazil.
Cellular automata model for gene networks
Physical review, Mar 1, 1997
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Papers by Daniel Stariolo