Interfacial segregation of interacting vacancies and their role on the wetting critical properties of the Blume-Emery-Griffiths model.

We study the wetting critical behavior of the three-state (s=±1,0) Blume-Emery-Griffiths model using numerical simulations. This model provides a suitable scenario for the study of the role of vacancies on the wetting behavior of a thin magnetic film. To this aim we study a system confined between parallel walls with competitive short-range surface magnetic fields (h_{L}=-|h_{1}|). We locate relevant critical curves for different values of the biquadratic interaction and use a thermodynamic integration method to calculate the surface tension as well as the interfacial excess energy and determine the wetting transition. Furthermore, we also calculate the local position of the interface along the film and its fluctuations (capillary waves), which are a measure of the interface width. To characterize the role played by vacancies on the interfacial behavior we evaluate the excess density of vacancies, i.e., the density difference between a system with and without interface. We also show that the temperature dependence of both the local position of the interface and its width can be rationalized in term of a finite-size scaling description, and we propose and successfully test the same scaling behavior for the average position of the center of mass of the vacancies and its fluctuations. This shows that the excess of vacancies can be associated to the presence of the interface that causes the observed segregation. This segregation phenomena is also evidenced by explicitly evaluating the interfacial free energy.

First- and second-order wetting transitions in confined Ising films in the presence of nonmagnetic impurities: a Monte Carlo simulation study.

In this work, we present the results of a systematic exploration of the effect caused by the introduction of nonmagnetic impurities (or defects) on the stabilization of the interface between two magnetic domains of opposite magnetic orientation. Those defects are simulated as spin vacancies along the center of confined two-dimensional Ising films, which have competing magnetic fields acting on the confinement walls. The calculations are performed for different L×M film sizes and by using the standard Metropolis dynamics. In the absence of defects, the film is characterized by an interface running along the M direction, which is induced by the competing surface fields. That interface undergoes a localization-delocalization transition that is the precursor of a true wetting transition taking place in the thermodynamic limit. When the density of defects is relatively low, our results show that the wetting phase transition is of second order, as in the absence of defects. On the other hand, when the density of nonmagnetic impurities is relatively high, a pinning effect of the interface gives rise to a first-order wetting phase transition. The observed transitions are characterized by measuring relevant properties, such as magnetization profiles, cumulants, magnetization fluctuations, etc., as a function of the density of defects. So, our main finding is that the presence of nonmagnetic impurities introduces a rich physical scenery, such as a line of second-order wetting transitions (observed for low density of defects) that merges into a first-order one just at a tricritical point. Precisely, these two latter findings are the major contributions of our study.

Effective multidimensional crossover behavior in a one-dimensional voter model with long-range probabilistic interactions.

A variant of the standard voter model, where a randomly selected site of a one-dimensional lattice (d=1) adopts the state of another site placed at a distance r from the previous one, is proposed and studied by means of numerical simulations that are rationalized with the aid of dynamical and finite-size scaling arguments. The distance between the two sites is also selected randomly with a probability given by P(r)∝r(-(d+σ)), where σ is a control parameter. In this way one can study how the introduction of these long-range interactions influences the dynamic behavior of the standard voter model with nearest-neighbor interactions. It is found that the dynamics strongly depends on the range of the interactions, which is parameterized by σ, leading to an interesting effective multidimensional crossover behavior, as follows. (a) For σ<1 ordering is no longer observed and the average interface density [ρ(t)] assumes a steady state in the thermodynamic limit. Instead, for finite-size systems an exponential decay with a characteristic time (τ) that increases with the size is observed. This behavior resembles the scenario corresponding to the short-range voter model for d>2, as well as the case of both scale-free and small-world networks. (b) For σ>1, an ordering dynamics is observed, such that ρ(t)∝t(-α), where the exponent α increases with σ until it reaches the value α=1/2 for σ≥5, which corresponds to the behavior of the standard voter model with short-range interactions in d=1. (c) Finally, for σ≈1 we show evidence of a critical-type behavior as in the case of the critical dimension (d(c)=2) of the standard voter model.

Topological effects on the absorbing phase transition of the contact process in fractal media.

In a recent paper [S. B. Lee, Physica A 387, 1567 (2008)] the epidemic spread of the contact process (CP) in deterministic fractals, already studied by I. Jensen [J. Phys. A 24, L1111 (1991)], has been investigated by means of computer simulations. In these previous studies, epidemics are started from randomly selected sites of the fractal, and the obtained results are averaged all together. Motivated by these early works, here we also studied the epidemic behavior of the CP in the same fractals, namely, a Sierpinski carpet and the checkerboard fractals but averaging epidemics started from the same site. These fractal media have spatial discrete scale invariance symmetry, and consequently the dynamic evolution of some physical observables may become coupled to the topology, leading to the logarithmic-oscillatory modulation of the corresponding power laws. In fact, by means of extensive simulations we shown that the topology of the substrata causes the oscillatory behavior of the epidemic observables. However, in order to observe these oscillations, which have not been reported in earlier works, the interference effect arising during the averaging of epidemics started from nonequivalent sites should be eliminated. Finally, by analyzing our data and those available on the literature for the dependence of the exponents eta and delta on the dimensionality of substrata, we conjectured that for integer dimensions (2

Dynamical behavior of three-dimensional confined Ising systems with short- and long-range competing surface fields.

The dynamical behavior of ferromagnetic Ising films confined in a DxLxL geometry (D<

Discrete scale invariance effects in the nonequilibrium critical behavior of the Ising magnet on a fractal substrate.

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension d(H)=1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. We have obtained evidence showing that during these relaxation processes both the growth and the fragmentation of magnetic domains become influenced by the hierarchical structure of the substrate. In fact, the interplay between the dynamic behavior of the magnet and the underlying fractal leads to the emergence of a logarithmic-periodic oscillation, superimposed to a power law, which has been observed in the time dependence of both the decay of the magnetization and its logarithmic derivative. These oscillations have been carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The effects of the substrate can also be observed from the dependence of the effective critical exponents on the segmentation step. The exponent theta of the initial increase of the magnetization has also been obtained and the results suggest that it would be almost independent of the fractal dimension of the substrate, provided that d(H) is close enough to d=2. The oscillations have been discussed within the framework of the discrete scale invariance of the substrate.

Critical behavior of an Ising system on the Sierpinski carpet: a short-time dynamics study.

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent theta of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent theta exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent z shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.

Theoretical description of teaching-learning processes: a multidisciplinary approach.

A multidisciplinary approach based on concepts from sociology, educational psychology, statistical physics, and computational science is developed for the theoretical description of teaching-learning processes that take place in the classroom. The emerging model is consistent with well-established empirical results, such as the higher achievements reached working in collaborative groups and the influence of the structure of the group on the achievements of the individuals. Furthermore, another social learning process that takes place in massive interactions among individuals via the Internet is also investigated.

Critical and oscillatory behavior of a system of smart preys and predators.

It is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey-predator coexistence and an state where predator extinction is observed. Within the coexistence regime, the system exhibits a transition between a regime where the densities of species remain constant and another with self-sustained oscillations, respectively. This transition is located by means of a combined treatment involving finite-size scaling and Fourier transforms. Furthermore, it is shown that the transition can be rationalized in terms of the standard percolation theory. The existence of an oscillatory regime in the thermodynamic limit, which is in contrast to previous findings of Boccara et al. [Phys. Rev. E 50, 4531 (1994)], may be due to subtle differences between the studied models.

Comparative study of an Eden model for the irreversible growth of spins and the equilibrium Ising model.

The magnetic Eden model (MEM) [N. Vandewalle and M. Ausloos, Phys. Rev. E 50, R635 (1994)] with ferromagnetic interactions between nearest-neighbor spins is studied in (d+1)-dimensional rectangular geometries for d=1,2. In the MEM, magnetic clusters are grown by adding spins at the boundaries of the clusters. The orientation of the added spins depends on both the energetic interaction with already deposited spins and the temperature, through a Boltzmann factor. A numerical Monte Carlo investigation of the MEM has been performed and the results of the simulations have been analyzed using finite-size scaling arguments. As in the case of the Ising model, the MEM in d=1 is noncritical (only exhibits an ordered phase at T=0). In d=2 the MEM exhibits an order-disorder transition of second order at a finite temperature. Such transition has been characterized in detail and the relevant critical exponents have been determined. These exponents are in agreement (within error bars) with those of the Ising model in two dimensions. Further similarities between both models have been found by evaluating the probability distribution of the order parameter, the magnetization, and the susceptibility. Results obtained by means of extensive computer simulations allow us to put forward a conjecture that establishes a nontrivial correspondence between the MEM for the irreversible growth of spins and the equilibrium Ising model. This conjecture is certainly a theoretical challenge and its confirmation will contribute to the development of a framework for the study of irreversible growth processes.

Competitive growth model involving random deposition and random deposition with surface relaxation.

A deposition model that considers a mixture of random deposition with surface relaxation and a pure random deposition is proposed and studied. As the system evolves, random deposition with surface relaxation (pure random deposition) take place with probability p and (1-p), respectively. The discrete (microscopic) approach to the model is studied by means of extensive numerical simulations, while continuous equations are used in order to investigate the mesoscopic properties of the model. A dynamic scaling ansatz for the interface width W(L,t,p) as a function of the lattice side L, the time t and p is formulated and tested. Three exponents, which can be linked to the standard growth exponent of random deposition with surface relaxation by means of a scaling relation, are identified. In the continuous limit, the model can be well described by means of a phenomenological stochastic growth equation with a p-dependent effective surface tension.

Numerical study of persistence in models with absorbing states.

Extensive Monte Carlo simulations are performed in order to evaluate both the local (straight theta(l)) and global (straight theta(g)) persistence exponents in the Ziff-Gulari-Barshad (ZGB) [Phys. Rev. Lett. 56, 2553 (1986)] irreversible reaction model. At the second-order irreversible phase transition (IPT) we find that both the local and the global persistence exhibit power-law behavior with a crossover between two different time regimes. On the other hand, at the ZGB first-order IPT, active sites are short lived and the persistence decays more abruptly; it is not clear whether it shows power-law behavior or not. In order to analyze universality issues, we have also studied another model with absorbing states, the contact process, and evaluated the local persistence exponent in dimensions from 1 to 4. A striking apparent superuniversality is reported: the local persistence exponent seems to coincide in both one- and two-dimensional systems. Some other aspects of persistence in systems with absorbing states are also analyzed.

Irreversible phase transitions driven by an oscillatory parameter in a far-from-equilibrium system.

The dynamic response of a forest-fire model to the harmonic variation of an external parameter is studied by means of numerical simulations. Second-order irreversible phase transitions driven by the harmonic input are reported. The location of such transitions depends on both the amplitude and period of the input signal. By means of epidemic studies the relevant critical exponents can be determined, which allow us to place the reported transitions in the universality class of directed percolation. This conclusion is also supported by a field theoretical calculation.