Stability of vacuum in coupled directed percolation processes

TL;DR

This paper investigates the stability of the vacuum in coupled directed percolation processes with multiple species, revealing the role of annihilation and coupling in phase transitions and critical behavior.

Contribution

It demonstrates how spontaneous annihilation stabilizes the vacuum and analyzes the effects of coupling and interactions on phase stability and critical exponents.

Findings

Vacuum stability depends on the type of process and coupling strength.

In coupled contact processes, the vacuum remains stable with DP transitions.

In coupled BAW, the vacuum can become unstable under strong coupling.

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, $\beta=\nu_{\bot}=1/2$ and $\nu_{||}=1$, regardless of the presence of HC interaction. We also discuss the effects of the asymmetric coupling.