Critical behavior of an even-offspringed branching and annihilating random-walk cellular automaton with spatial disorder

Particle-density fluctuations and universality in the conserved stochastic sandpile

We examine fluctuations in particle density in the restricted-height, conserved stochastic sandpile (CSS). In this and related models, the global particle density is a temperaturelike control parameter. Thus local fluctuations in this density correspond to disorder; if this disorder is a relevant perturbation of directed percolation (DP), then the CSS should exhibit non-DP critical behavior. We analyze the scaling of the variance Vℓ of the number of particles in regions of ℓd sites in extensive simulations of the quasistationary state in one and two dimensions. Our results, combined with a Harris-like argument for the relevance of particle-density fluctuations, strongly suggest that conserved stochastic sandpiles belong to a universality class distinct from that of DP.

Universality class of the conserved Manna model in one dimension

The nonequilibrium absorbing phase transition of the discrete conserved Manna model was studied via Monte Carlo simulations on a one-dimensional chain, using the natural initial states with a sequential update. The critical density of the particles was found to be smaller than the recently reported value, and the order-parameter exponent was considerably different from the directed percolation (DP) value. The influence of quenched disorder was also studied on a diluted strip of L_{x}×L_{y} lattice sites with L_{x}≫L_{y}, and the results were compared with those of the contact process (CP). It was found that the Manna model and the CP exhibited distinctly different behaviors; the CP exhibited nonuniversal power-law decreases of active-site densities in the Griffith phase, whereas the Manna model showed a standard critical behavior. These results consistently suggest that the Manna model belongs to a universality class that is different from the DP class.

Nonuniversal disordered Glauber dynamics

We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the nonuniversal values of those of plain dimerized chains. In the second situation their values are still nonuniversal and subdiffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.

Phase diagram for a zero-temperature Glauber dynamics under partially synchronous updates

We consider generalized zero-temperature Glauber dynamics under a partially synchronous updating mode for a one-dimensional system. Using Monte Carlo simulations, we calculate the phase diagram and show that the system exhibits phase transition between the ferromagnetic and active antiferromagnetic phases. Moreover, we provide analytical calculations that allow us to understand the origin of the phase transition and confirm simulation results obtained earlier for synchronous updates.

Random fields at a nonequilibrium phase transition

We study nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such random-field disorder is known to have dramatic effects: it prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we show that the phase transition of the one-dimensional generalized contact process persists in the presence of random-field disorder. The ultraslow dynamics in the symmetry-broken phase is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by large-scale Monte Carlo simulations.

Determination of the critical exponents for absorbing phase transitions in the conserved lattice gas model in three dimensions

The critical exponents were measured for absorbing phase transitions in the conserved lattice gas (CLG) model on a simple cubic lattice. The correlation-length exponent calculated from the dynamic exponent obtained by finite-size scaling and from the mean spreading distance was consistently found to be ν(⊥)=0.631±0.02, which yields a positive specific heat exponent α=2-dν(⊥) on a pure system. The pure fixed point should, thus, be unstable if the Harris criterion established in equilibrium systems is applicable to the nonequilibrium absorbing phase transitions of the CLG model. However, this prediction is in contradiction with recent simulation results.

Phase transitions of the generalized contact process with two absorbing states

We investigate the generalized contact process with two absorbing states in one space dimension by means of large-scale Monte Carlo simulations. Treating the creation rate of active sites between inactive domains as an independent parameter leads to a rich phase diagram. In addition to the conventional active and inactive phases we find a parameter region where the simple contact process is inactive, but an infinitesimal creation rate at the boundary between inactive domains is sufficient to take the system into the active phase. Thus, the generalized contact process has two different phase transition lines. The point separating them shares some characteristics with a multicritical point. We also study in detail the critical behaviors of these transitions and their universality.

Crossovers from parity conserving to directed percolation universality

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric absorbing phases (the cellular automaton version of the nonequilibrium kinetic Ising model (NEKIMCA) and a stochastic cellular automaton invented by Grassberger, Krause, and von der Twer [J. Phys. A 17, L105 (1984)]) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/phi approximately equal to 0.53(2) . In the case of a branching and annihilating random walk model with an even number of offspring (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/phi approximately equal to 0.205(5) . The two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These subclasses differ in cluster scaling exponents.

One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one-dimensional, nonequilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for "+" and "-" spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of + and - spins, and of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar [Phys Rev. Lett 86, 2301 (2001)]. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero [Phys Rev. E 57, 5060 (1998)]. We also show that the isotropic two-component AB --> [symbol: see text] model is insensitive to reaction disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.

Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture

We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active/inactive synchronization patches. Systematic computer simulations involving 2(30) initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of interfaces delimiting active/inactive patches. Such interfaces are studied with a sidewise spatial updating algorithm. This novel tool allows us to prove that the interfaces found empirically are the only interfaces possible for these periods, independently of the size of the automata. The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice.