Discontinuous Transition in a Boundary Driven Contact Process

TL;DR

This paper investigates a boundary-driven contact process with bias, revealing a discontinuous phase transition characterized by traveling wave behavior and linking wave properties to directed percolation critical exponents.

Contribution

It introduces a modified Fisher equation to explain the discontinuous transition and connects wave dynamics with DP universality class properties.

Findings

Wave velocity is discontinuous at the transition

Traveling waves occur in the supercritical phase

Discontinuity explained by a modified Fisher equation

Abstract

The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an active wall. This model exhibits waves of activity emanating from the active wall and, when the system is supercritical, propagating indefinitely as travelling (Fisher) waves. In the subcritical phase the activity is localised near the wall. We study the phase transition numerically and show that certain properties of the system, notably the wave velocity, are discontinuous across the transition. Using a modified Fisher equation to model the system we elucidate the mechanism by which the the discontinuity arises. Furthermore we establish relations between properties of the travelling wave and DP critical exponents.