Boundary-Induced Nonequilibrium Phase Transition into an Absorbing State

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example, we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.

Figure 1

Definition of the model: Particles diffuse on a semi-infinite one-dimensional chain according to a symmetric exclusion process. The only exception is the leftmost site, where particles multiply and annihilate as in a contact process.

Figure 2

Typical temporal evolution of the model at criticality, starting with a single particle at the leftmost site. The color scale visualizes the particle density. At the leftmost site, one observes intermittent bursts of activity.

Figure 3

Numerical simulation of the process starting with a single active site at the origin for different values of $\Delta =p-p_c$. The graphs show the density at the leftmost site ${\rho }_0(t)$, the survival probability $P_s(t)$, and the number of particles $⟨N(t)⟩$ averaged over all runs, respectively.

Figure 4

Left: Data collapse of the rescaled profiles of the particle density at criticality for $t_0=64,128,\dots ,8192$ (blue) compared to a Gaussian distribution (red). Inset: The same data collapse in a double-logarithmic representation. Right: Density of particles (blue) and pairs (green) at $t_0={10}^6$, demonstrating the presence of correlations which decay in space as $x^{-1/2}$, indicating that $\beta /{\nu }_{\perp }=1/2$.