Pablo M. Gleiser

Self-organized criticality in a model of biological evolution with long-range interactions

In this work we study the effects of introducing long-range interactions in the Bak–Sneppen (BS) model of biological evolution. We analyze a recently proposed version of the BS model where the interactions decay as r−α; in this way, the first nearest neighbors model is recovered in the limit α→∞, and the random neighbors version for α=0. We study the space and time correlations and analyze how the critical behavior of the system changes with the parameter α. We also study the sensibility to initial conditions of the model using the spreading of damage technique. We found that the system displays several distinct critical regimes as α is varied from α=0 to α→∞.

Metastable states in a two-dimensional Ising model with dipolar interactions

Abstract The equilibrium phase diagram of a two-dimensional Ising model with competing exchange and dipolar interactions is analyzed using a Monte Carlo simulation technique. We consider the low temperature region of the (δ,T) phase diagram (δ being the ratio between the strengths of the exchange and dipolar interactions) for the range of values of δ where striped phases with widths h=1 and 2 are present. We show that the transition line between both phases is a first order one. We also show that, associated with the first-order phase transition, there appear metastable states of the phase h=2 in the region where the phase h=1 is the thermodynamically stable one and vice versa.

Slow dynamics in a 2D Ising model with competing interactions

The far-from-equilibrium low-temperature dynamics of ultrathin magnetic films is analyzed by using Monte Carlo numerical simulations on a two-dimensional Ising model with competing exchange (J 0 ) and dipolar (J d ) interactions. In particular, we focus our attention on the low-temperature region of the (δ,T) phase diagram (where δ=J 0 /J d ) for the range of values of S where striped phases with widths h=I (h I ) and h=2 (h2) are present. The presence of metastable states of the phase h2 in the region where the phase h 1 is the thermodynamically stable one and vice versa was established recently. In this work we show that the presence of these metastable states appears as a blocking mechanism that slows the dynamics of magnetic domain growth when the system is quenched from a high-temperature state to a low-temperature state in the region of metastability.

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 r(-rho), r being the distance traveled by a grain in a single toppling event. The exponent rho controls the average rolling distance. We have shown that the crossover from the power law to the 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 1<rho<2, 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 rho>2, where the average rolling distance is independent of the system size.

Damage spreading in a rice pile model

In a recent experiment with rice piles [V. Frette et al., Nature 379 (1996) 49] it was observed that the distribution of avalanches presents a power-law behavior for elongated rice, while avalanches for round rice present a characteristic length. These experiments showed that granular piles may display Self-Organized Criticality (SOC), but the behavior is not universal. We have recently presented a model for granular flow in a one-dimensional rice pile [P.M. Gleiser et al., Phys. Rev. E, in press] which exhibits the crossover from power law to stretched exponential behavior observed experimentally in the granular dynamics of rice piles. In this work, we use the damage spreading technique to study how a small perturbation (or damage) propagates through the system.

Dynamical heterogeneities as fingerprints of a backbone structure in Potts models.

We investigate slow nonequilibrium dynamical processes in a two-dimensional q-state Potts model with both ferromagnetic and ±J couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This quantity is known for clearly unveiling dynamical heterogeneities. Using a two-times protocol we characterize the different time scales observed and relate them to growth processes occurring in the system. In particular we target the possible relation between the different time scales and the spatial heterogeneities originated in the ground-state topology, which are associated to the presence of a backbone structure. We perform numerical simulations using an approach based on graphis processing units (GPUs) which permits us to reach large system sizes. We present evidence supporting both the idea of a growing process in the preasymptotic regime of the glassy phases and the existence of a backbone structure behind this process.

Dynamical properties of the hypercell spin-glass model

The spreading of damage technique is used to study the dynamical phase diagram of the spin-glass hypercubic cell model in a heat bath Monte Carlo simulation. Since the hypercubic cell in dimension

ULTRA-THIN MAGNETIC FILMS AND THE STRUCTURAL GLASS TRANSITION: A MODELLING ANALOGY

2D

Intertemporal Distributions Of A Rice Pile Model

and the hypercubic lattice in dimension

Two dimensional Ising model with long-range competing interactions

D