Nonuniversal Critical Spreading in Two Dimensions

Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary continuously with the density phi in the surrounding region. The exponent delta changes by more than an order of magnitude, and eta changes sign. The location of the critical point also depends on phi, which has important implications for scaling. As expected on the basis of universality, the static critical behavior belongs to the directed percolation class.Comment: 21 pages, REVTeX, figures available upon reques

Interacting Monomer-Dimer Model with Infinitely Many Absorbing States

We study a modified version of the interacting monomer-dimer (IMD) model that has infinitely many absorbing (IMA) states. Unlike all other previously studied models with IMA states, the absorbing states can be divided into two equivalent groups which are dynamically separated infinitely far apart. Monte Carlo simulations show that this model belongs to the directed Ising universality class like the ordinary IMD model with two equivalent absorbing states. This model is the first model with IMA states which does not belong to the directed percolation (DP) universality class. The DP universality class can be restored in two ways, i.e., by connecting the two equivalent groups dynamically or by introducing a symmetry-breaking field between the two groups.Comment: 5 pages, 5 figure

Criticality of natural absorbing states

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating random walk with $N\geq 2$ species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power law singularities which signal the approach of the critical point. These results are also explained using random walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum finding procedure, it has the best efficiency very close to the critical point.Comment: 6 page

Numerical Study of a Field Theory for Directed Percolation

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00

Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model

We study a three species monomer-monomer catalytic surface reaction model with a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one species. The transition from the reactive to a saturated phase shows directed percolation critical behavior. Each pair of these reactive-saturated phase boundaries join at a bicritical point where the universal behavior is in the even branching annihilating random walk class. We find the crossover exponent from bicritical to critical behavior and a new exponent associated with the bicritical interface dynamics.Comment: 4 pages RevTex. 4 eps figures included with psfig.sty. Uses multicol.sty. Accepted for publication in PR

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only.Comment: 11 pages, 21 figures, Revtex, submitted to Phy. Rev.

Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions

The damage spreading (DS) transitions of two one-dimensional stochastic cellular automata suggested by Grassberger (A and B) and the kinetic Ising model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and spins. On the level of spins the parity conservation is not satisfied and therefore studying these models provides a convenient tool to understand the dependence of DS properties on symmetries. For the model B the critical point and the DS transition point is well separated and directed percolation damage spreading transition universality was found for spin damage as well as for kink damage in spite of the conservation of damage variables modulo 2 in the latter case. For the A stochastic cellular automaton, and the NEKIM model the two transition points coincide with drastic effects on the damage of spin and kink variables showing different time dependent behaviours. While the kink DS transition is continuous and shows regular PC class universality, the spin damage exhibits a discontinuous phase transition with compact clusters and PC like dynamical scaling ($\eta^,$), ($\delta_s$) and ($z_s$) exponents whereas the static exponents determined by FSS are consistent with that of the spins of the NEKIM model at the PC transition point. The generalised hyper-scaling law is satisfied.Comment: 11 pages, 20 figures embedded in the text, minor changes in the text, a new table and new references are adde

One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate

The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR

The three species monomer-monomer model: A mean-field analysis and Monte Carlo study

We study the phase diagram and critical behavior of a one dimensional three species monomer-monomer surface reaction model. Static Monte Carlo simulations show a phase diagram consisting of a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one monomer species. The transitions from the reactive to saturated phases are all continuous, while the transitions between poisoned phases are first-order, with bicritical points where the reactive phase meets two poisoned phases. A mean-field cluster analysis predicts all of the qualitative features of the phase diagram only when correlations up to triplets of adjacent sites are included. Dynamic Monte Carlo simulations show that the transition from the reactive to a saturated phase show critical behavior in the directed percolation universality class, while the bicritical point shows critical behavior in the even branching annihilating random walk class. The crossover from bicritical to critical behavior is also studied.Comment: 16 pages using RevTeX, plus 10 figures. Uses psfig.st

Mean-Field Analysis and Monte Carlo Study of an Interacting Two-Species Catalytic Surface Reaction Model

We study the phase diagram and critical behavior of an interacting one dimensional two species monomer-monomer catalytic surface reaction model with a reactive phase as well as two equivalent adsorbing phase where one of the species saturates the system. A mean field analysis including correlations up to triplets of sites fails to reproduce the phase diagram found by Monte Carlo simulations. The three phases coexist at a bicritical point whose critical behavior is described by the even branching annihilating random walk universality class. This work confirms the hypothesis that the conservation modulo 2 of the domain walls under the dynamics at the bicritical point is the essential feature in producing critical behavior different from directed percolation. The interfacial fluctuations show the same universal behavior seen at the bicritical point in a three-species model, supporting the conjecture that these fluctuations are a new universal characteristic of the model.Comment: 11 pages using RevTeX, plus 4 Postscript figures. Uses psfig.st