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 that 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. ͓S1063-651X͑98͒06806-8͔

It has been generally believed that hardcore interaction is irrelevant to absorbing type critical phenomena because the particle density is so low near an absorbing phase transition. We study the effect of hardcore interaction on the N species branching annihilating random walks with two offspring and report that hardcore interaction drastically changes the absorbing type critical phenomena in a nontrivial way. Through Langevin equation type approach, we predict analytically the values of the scaling exponents, ν ⊥ = 2, z = 2, α = 1/2, β = 2 in one dimension for all N > 1. Direct numerical simulations confirm our prediction. When the diffusion coefficients for different species are not identical, ν ⊥ and β vary continuously with the ratios between the coefficients.The study of nonequilibrium systems with trapped (absorbing) states has been very active in recent years [1]. Models displaying absorbing phase transitions describe a wide range of phenomena, in particular, epidemic spreading, catalytic chemical reactions, and transport in disordered media. Furthermore, the absorbing transition is one of the simplest and natural extensions of the well-established equilibrium phase transition to nonequilibrium systems, which are still poorly understood.The concept of universality, which plays a key role in equilibrium critical phenomena, was shown to be applicable also to nonequilibrium absorbing transitions. Critical behavior near an absorbing transition is determined by properties such as dimensionality and symmetry, and is not affected by details of the system. Finding a new universality class is difficult, and only a few classes of absorbing transitions are known [1].Hardcore interaction between particles or kinks has been believed to be irrelevant to absorbing type critical phenomena, because the particle density is so low near an absorbing transition that the probability of multiple occupations at a site should be too small to be significant. This conventional belief leads to recent successes of field theoretical techniques using bosonic type operators [2][3][4][5][6]. However, it is well known that hardcore interaction does changes the asymptotic decay behavior of the particle density in many multi-species diffusion-reaction models near an annihilation fixed point [7]. Since many absorbing transition models can be mapped onto diffusionreaction ones, it may seem natural to ask a question whether hardcore constraint changes the absorbing type universality classes in multi-species models. Despite recent efforts using fermionic formulation incorporating hardcore interactions [8,9], the effect of hardcore interactions is barely understood both analytically and numerically.In this Letter, we study the N species branching annihilating random walks with two offspring (N -BAW(2)), introduced recently by Cardy and Täuber [6]. The model was solved exactly for all N > 1, using renormalization group techniques in bosonic type formulation which ignores hardcore interactions. We employ Langevin equation type approach incorporat...

We investigate the phase diagram of branching annihilating random walks with one and two offsprings in one dimension. A walker can hop to a nearest neighbor site or branch with one or two offsprings with relative ratio. Two walkers annihilate immediately when they meet. In general, this model exhibits a continuous phase transition from an active state into the absorbing state (vacuum) at a finite hopping probability. We map out the phase diagram by Monte Carlo simulations which shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two-offspring branching process increases. This reentrant property apparently contradicts the conventional wisdom that increasing the number of offsprings will tend to make the system more active. We show that the reentrant property is due to the static reflection symmetry of two-offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one.PACS numbers: 05.70.Ln, 82.65.Jv

We investigate condensation phase transitions of the symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution P(k) approximately k(-gamma). In the SCA model, masses diffuse with unit rate, and unit mass chips off from mass with rate omega. The dynamics conserves total mass density rho. In the steady state, on RNs and SFNs with gamma > 3 for omega is not equal to infinity, we numerically show that the SCA model undergoes the same type of condensation transitions as those on regular lattices. However, the critical line rho(c)(omega) depends on network structures. On SFNs with gamma < or = 3, the fluid phase of exponential mass distribution completely disappears and no phase transitions occurs. Instead, the condensation with exponentially decaying background mass distribution always takes place for any nonzero density. For the existence of the condensed phase for gamma < or = 3 at the zero density limit, we investigate one lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives indefinitely with finite survival probability on RNs and SFNs with gamma > 3, and dies out exponentially on SFNs with gamma< or = 3. The finite lifetime of a lamb on SFNs with gamma < or = 3 ensures the existence of the condensation at the zero density limit on SFNs with gamma < or = 3, at which direct numerical simulations are practically impossible. At omega = infinity, we numerically confirm that complete condensation takes place for any rho > 0 on RNs. Together with the recent study on SFNs, the complete condensation always occurs on both RNs and SFNs in zero range process with constant hopping rate.