Short-time dynamics in active systems: the Vicsek model.

We study the short-time dynamics (STD) of the Vicsek model (VM) with vector noise. The study of STD has proved to be very useful in the determination of the critical point, critical exponents and spinodal points in equilibrium phase transitions. Here we aim is to test its applicability in active systems. We find that, despite the essential non-equilibrium characteristics of the VM (absence of detailed balance, activity), the STD presents qualitatively the same phenomenology as in equilibrium systems. From the STD one can distinguish whether the transition is continuous or discontinuous (which we have checked also computing the Binder cumulant). When the transition is continuous, one can determine the critical point and the critical exponents.

Noisy multistate voter model for flocking in finite dimensions.

We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two-dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle within a distance R=1, with the addition of a perturbation of amplitude η (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude η. In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise η>0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for η=0 full order is eventually achieved for a system with any number of particles N. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise (η>0). We show that the finite-size transition noise vanishes with N as η_{c}^{1D}∼N^{-1} and η_{c}^{2D}∼(NlnN)^{-1/2} in one- and two-dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude η_{c}>0 that is proportional to v, and that scales approximately as η_{c}∼v(-lnv)^{-1/2} for v≪1. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.

Multistate voter model with imperfect copying.

The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N. In the case of perfect copying η=0, the system reaches an absorbing configuration with complete order (ψ=1) for all values of N. However, for any degree of imperfection η>0, we show that the average value of ψ at the stationary state decreases with N as 〈ψ〉≃6/(π^{2}η^{2}N) for η≪1 and η^{2}N≳1, and thus the system becomes totally disordered in the thermodynamic limit N→∞. We also show that 〈ψ〉≃1-π^{2}/6η^{2}N in the vanishing small error limit η→0, which implies that complete order is never achieved for η>0. These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.

Stability limits for the supercooled liquid and superheated crystal of Lennard-Jones particles.

We have studied the limits of stability in the first order liquid-solid phase transition in a Lennard-Jones system by means of the short-time relaxation method and using the bond-orientational order parameter Q6. These limits are compared with the melting line. We have paid special attention to the supercooled liquid, comparing our results with the point where the free energy cost of forming a nucleating droplet goes to zero. We also indirectly estimate the dimension associated to the critical nucleus at the spinodal, expected to be fractal according to mean field theories of nucleation.

Spinodals and critical point using short-time dynamics for a simple model of liquid.

We have applied the short-time dynamics method to the gas-liquid transition to detect the supercooled gas instability (gas spinodal) and the superheated liquid instability (liquid spinodal). Using Monte Carlo simulation, we have obtained the two spinodals for a wide range of pressure in sub-critical and critical conditions and estimated the critical temperature and pressure. Our method is faster than previous approaches and allows studying spinodals without needing equilibration of the system in the metastable region. It is thus free of the extrapolation problems present in other methods, and in principle could be applied to systems such as glass-forming liquids, where equilibration is very difficult even far from the spinodal. We have also done molecular dynamics simulations, where we find the method again able to detect the both spinodals. Our results are compared with different previous results in the literature and show a good agreement.

Aging and crystallization in a lattice glass model.

We have studied the three-dimensional lattice glass of Pica Ciamarra et al. [Phys. Rev. E 67, 057105 (2003)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times, and aging. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower than 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.

Stochastic resonance and dynamic first-order pseudo-phase-transitions in the irreversible growth of thin films under spatially periodic magnetic fields.

We study the irreversible growth of magnetic thin films under the influence of spatially periodic fields by means of extensive Monte Carlo simulations. We find first-order pseudo-phase-transitions that separate a dynamically disordered phase from a dynamically ordered phase. By analogy with time-dependent oscillating fields applied to Ising-type models, we qualitatively associate this dynamic transition with the localization-delocalization transition of spatial hysteresis loops. Depending on the relative width of the magnetic film L compared to the wavelength of the external field λ, different transition regimes are observed. For small systems (L < λ), the transition is associated with the standard stochastic resonance regime, while for large systems (L > λ), the transition is driven by anomalous stochastic resonance. The origin of the latter is identified as due to the emergence of an additional relevant length scale, namely, the roughness of the spin domain switching interface. The distinction between different stochastic resonance regimes is discussed at length both qualitatively by means of snapshot configurations and quantitatively via residence-length and order-parameter probability distributions.

Phase diagram of a cyclic predator-prey model with neutral-pair exchange.

In this paper we obtain the phase diagram of a four-species predator-prey lattice model by using the proposed gradient method. We consider cyclic transitions between consecutive states, representing invasion or predation, and allowed the exchange between neighboring neutral pairs. By applying a gradient in the invasion rate parameter one can see, in the same simulation, the presence of two symmetric absorbing phases, composed by neutral pairs, and an active phase that includes all four species. In this sense, the study of a single-valued interface and its fluctuations give the critical point of the irreversible phase transition and the corresponding universality classes. Also, the consideration of a multivalued interface and its fluctuations bring the percolation threshold. We show that the model presents two lines of irreversible first-order phase transition between the two absorbing phases and the active phase. Depending on the value of the system parameters, these lines can converge into a triple point, which is the beginning of a first-order irreversible line between the two absorbing phases, or end in two critical points belonging to the directed percolation universality class. Standard simulations for some characteristic values of the parameters confirm the order of the transitions as determined by the gradient method. Besides, below the triple point the model presents two standard percolation lines in the active phase and above a first-order percolation transition as already found in other similar models.

Phase diagram and critical behavior of a forest-fire model in a gradient of immunity.

The forest-fire model with immune trees (FFMIT) is a cellular automaton early proposed by Drossel and Schwabl [Physica A 199, 183 (1993)], in which each site of a lattice can be in three possible states: occupied by a tree, empty, or occupied by a burning tree (fire). The trees grow at empty sites with probability p, healthy trees catch fire from adjacent burning trees with probability (1-g), where g is the immunity, and a burning tree becomes an empty site spontaneously. In this paper we study the FFMIT by means of the recently proposed gradient method (GM), considering the immunity as a uniform gradient along the horizontal axis of the lattice. The GM allows the simultaneous treatment of both the active and the inactive phases of the model in the same simulation. In this way, the study of a single-valued interface gives the critical point of the active-absorbing transition, whereas the study of a multivalued interface brings the percolation threshold into the active phase. Therefore we present a complete phase diagram for the FFMIT, for all range of p, where, besides the usual active-absorbing transition of the model, we locate a transition between the active percolating and the active nonpercolating phases. The average location and the width of both interfaces, as well as the absorbing and percolating cluster densities, obey a scaling behavior that is governed by the exponent α=1/(1+ν), where ν is the suitable correlation length exponent (ν(⊥) for the directed percolation transition and ν for the standard percolation transition). We also show that the GM allows us to calculate the critical exponents associated with both the order parameter of the absorbing transition and the number of particles in the multivalued interface. Besides, we show that by using the gradient method, the collapse in a single curve of cluster densities obtained for samples of different side is a very sensitive method in order to obtain the critical points and the percolation thresholds.

Nonequilibrium characterization of spinodal points using short time dynamics.

Although intuitively appealing, the concept of spinodal is rigorously defined only in systems with infinite range interactions (mean-field systems). In short-range systems, a pseudospinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean-field systems and with the pseudospinodal point obtained by extrapolation of metaequilibrium behavior in short-range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.

Proposal and applications of a method for the study of irreversible phase transitions.

The gradient method for the study of irreversible phase transitions in far-from-equilibrium lattice systems is proposed and successfully applied to both the archetypical case of the Ziff-Gulari-Barshad model [R. M. Ziff, Phys. Rev. Lett. 56, 2553 (1986)] and a forest-fire cellular automaton. By setting a gradient of the control parameter along one axis of the lattice, one can simultaneously treat both the active and the inactive phases of the system. In this way different interfaces are defined whose study allows us to find the active-inactive phase transition (both of first and second order), as well as the description of the active phase as composed of two further phases: the percolating and the nonpercolating ones. The average location and the width of the interfaces obey standard scaling behavior that is essentially governed by the roughness exponent alpha=1/(1+nu) , where nu is the suitable correlation length exponent.

Interplay between thermal percolation and jamming upon dimer adsorption on binary alloys.

By means of Monte Carlo simulations we study jamming and percolation processes upon the random sequential adsorption of dimers on binary alloys with different degrees of structural order. The substrates are equimolar mixtures that we simulate using an Ising model with conserved order parameter. After an annealing at temperature T we quench the alloys to freeze the state of order of the surface at this temperature. The deposition is then performed neglecting thermal effects like surface desorption or diffusion. In this way, the annealing temperature is a continuous parameter that characterizes the adsorbing surfaces, shaping the deposition process. As the alloys undergo an order-disorder phase transition at the Onsager critical temperature (Tc), the jamming and percolating properties of the set of deposited dimers are subjected to nontrivial changes, which we summarize in a density-temperature phase diagram. We find that for TT*. Particular attention is focused close to T*, where the interplay between jamming and percolation restricts fluctuations, forcing exponents seemingly different from the standard percolation universality class. By analogy with a thermal transition, we study the onset of percolation using the temperature T as a control parameter. We propose thermal scaling Ansätze to analyze the behavior of the percolation threshold and its thermally induced fluctuations. Also, the fractal dimension of the percolating cluster is determined. Based on these measurements and the excellent data collapse, we conclude that the universality class of standard percolation is preserved for all temperatures.

Fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media.

The fluctuations of the jamming coverage upon random sequential adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by sigma(thetaJ)) decay with the lattice size according to the power law sigma(thetaJ) proportional, variant L(-1/nu). The exponent nu depends on the dimensionality D of the substrate and the fractal dimension of the set where the RSA process actually takes place (df) according to nu=2/(2D-df). This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.

Numerical study of a first-order irreversible phase transition in a CO+NO catalyzed reaction model.

The first-order irreversible phase transition (IPT) of the Yaldran-Khan model [Yaldran-Khan, J. Catal. 131, 369 (1991)] for the CO+NO reaction is studied using the constant-coverage (CC) ensemble and performing epidemic simulations. The CC method allows the study of hysteretic effects close to coexistence as well as the location of both the upper spinodal point and the coexistence point. Epidemic studies show that at coexistence the number of active sites decreases according to a (short-time) power law followed by a (long-time) exponential decay. It is concluded that first-order IPT's share many characteristics of their reversible counterparts, such as the development of short-ranged correlations, hysteretic effects, metastabilities, etc.