Stability of vacuum in coupled directed percolation processes

Abstract

We study the absorbing phase transitions in coupled directed percolation (DP) processes with $N$-species particles in one dimension. The interspecies coupling is linear, bidirectional, and excitatory. We find that the presence of a spontaneous annihilation process $A\to 0$ is essential in stabilizing the absorbing phase (vacuum). In the coupled contact processes, the vacuum is stable and the system exhibits DP type transitions, regardless of the coupling strength, for all $N$. However, in the coupled branching annihilation random walks with one offspring (BAW), where particle annihilations occur only through binary diffusion processes $A+A\to 0$, the vacuum becomes unstable with respect to an arbitrarily small branching rate in a sufficiently strong coupling regime for $N\ge 3$. The N=2 BAW exhibits the DP type transition for any coupling strength, but the inclusion of interspecies hard core (HC) interaction makes the vacuum unstable again and the system is always active in a strong coupling regime. Critical behavior near the zero branching point is characterized by the scaling exponents, $\beta ={\nu }_{\perp }=1/2$ and ${\nu }_{||}=1$, regardless of the presence of HC interaction. We also discuss the effects of the asymmetric coupling.

6 pages, 5 figures

References in corpus (14)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Theory of Branching and Annihilating Random Walks
• Field Theory of Branching and Annihilating Random Walks
• Stochastic Lattice Models with Several Absorbing States
• One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk
• Non-equilibrium phase transitions in one-dimensional kinetic Ising models
• Multicritical behavior in coupled directed percolation processes
• Critical phenomena of nonequilibrium dynamical systems with two absorbing states
• Critical behavior of an absorbing phase transition in an interacting monomer-dimer model
• Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes
• Does hardcore interaction change absorbing type critical phenomena?
• Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process
• Critical branching-annihilating random walk of two species
• The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion

Cited by in corpus (2)

• Asymmetrically coupled directed percolation systems
• Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension