Simulating systems with absorbing state transitions

Absorbing state phase transitions are of particular interest in non-equilbrium statistical physics due to their strong violation of detailed balance. Unfortunately, a simple Euler approach to discretizing the Langevin equation runs into difficulties as the order parameter often becomes negative, which would be unphysical in most physical situations where it models a density. I will present an elegant operator splitting method proposed by Dornic et al and use Directed Percolation as a worked example of its usage. Directed Percolation is perhaps the most ubiquitous of absorbing phase transitions and represents arguably the only robust non-equilibrium universality class to date.