Theory of the NO+CO surface reaction model

We derive a pair approximation (PA) for the NO+CO model with instantaneous reactions. For both the triangular and square lattices, the PA, derived here using a simpler approach, yields a phase diagram with an active state for CO-fractions y in the interval y_1 < y < y_2, with a continuous (discontinuous) phase transition to a poisoned state at y_1 (y_2). This is in qualitative agreement with simulation for the triangular lattice, where our theory gives a rather accurate prediction for y_2. To obtain the correct phase diagram for the square lattice, i.e., no active state, we reformulate the PA using sublattices. The (formerly) active regime is then replaced by a poisoned state with broken symmetry (unequal sub- lattice coverages), as observed recently by Kortluke et al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in which the active state persists, although reduced in extent, we report here the first qualitatively correct theory of the NO+CO model on the square lattice. Surface diffusion of nitrogen can lead to an active state in this case. In one dimension, the PA predicts that diffusion is required for the existence of an active state.Comment: 15 pages, 9 figure

Universal aspects of vacancy-mediated disordering dynamics: the effect of external fields

We investigate the disordering of an initially phase-segregated binary alloy, due to a highly mobile defect which couples to an electric or gravitational field. Using both mean-field and Monte Carlo methods, we show that the late stages of this process exhibit dynamic scaling, characterized by a set of exponents and scaling functions. A new scaling variable emerges, associated with the field. While the scaling functions carry information about the field and the boundary conditions, the exponents are universal. They can be computed analytically, in excellent agreement with simulation results.Comment: 15 pages, 6 figure

Monte Carlo simulation of subsurface ordering kinetics in an fcc-alloy model

Within the atom-vacancy exchange mechanism in a nearest-neighbor interaction model we investigate the kinetics of surface-induced ordering processes close to the (001) surface of an fcc A_3B-alloy. After a sudden quench into the ordered phase with a final temperature above the ordering spinodal, T_f > T_sp, the early time kinetics is dominated by a segregation front which propagates into the bulk with nearly constant velocity. Below the spinodal, T_f < T_sp, motion of the segregation wave reflects a coarsening process which appears to be slower than predicted by the Lifschitz-Allen-Cahn law. In addition, in the front-penetrated region lateral growth differs distinctly from perpendicular growth, as a result of the special structure of antiphase boundaries near the surface. Our results are compared with recent experiments on the subsurface ordering kinetics at Cu_3Au (001).Comment: 10 pages, 9 figures, submitted to Phys. Rev. B, in prin

Generalized Scaling for Models with Multiple Absorbing States

At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a transition into an absorbing state, which is capable of describing exponents which vary according to the initial configuration. The resulting hyperscaling relation is supported by simulations of two lattice models.Comment: Latex 9 page

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

The first-order irreversible phase transitions (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 characteristic of their reversible counterparts, such as the development of short ranged correlations, hysteretic effects, metastabilities, etc.Comment: 17 pages, 10 figure

Dimensional reduction in a model with infinitely many absorbing states

Using Monte Carlo method we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta=0.273(5) suggests that the model belongs to the (1+1) rather than (2+1) directed-percolation universality class. We also show that for a large class of absorbing states the dynamic Monte Carlo method leads to spurious dynamical transitions.Comment: 6 pages, 4 figures, Phys.Rev. E, Dec. 199

Critical behaviour of a surface reaction model with infinitely many absorbing states

In a recent letter [J. Phys. A26, L801 (1993)], Yaldram et al. studied the critical behaviour of a simple lattice gas model of the CO-NO catalytic reaction. The model exhibits a second order nonequilibrium phase transition from an active state into one out of infinitely many absorbing states. Estimates for the critical exponent $\beta$ suggested that the model belongs to a new universality class. The results reported in this article contradict this notion, as estimates for various critical exponents show that the model belongs to the universality class of directed percolation.Comment: 10p+5fig, LaTeX+fig in uuencoded P

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

Are Damage Spreading Transitions Generically in the Universality Class of Directed Percolation?

We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in the same universality class as directed percolation. We conjecture that also other damage spreading transitions should be in this universality class, unless they coincide with other transitions (as in the Ising model with Glauber dynamics) and provided the probability for a locally damaged state to become healed is not zero.Comment: 10 pages, LATE