Random field disorder at an absorbing state transition in one and two dimensions

TL;DR

This study explores how random-field disorder affects nonequilibrium phase transitions in one- and two-dimensional systems, revealing that it does not destroy the transition but alters the dynamics within the symmetry-broken phase.

Contribution

It demonstrates that random-field disorder does not eliminate the phase transition in these systems and provides a detailed analysis of the modified dynamics and universality class.

Findings

Random-field disorder does not destroy the phase transition in 1D and 2D.

In 1D, dynamics are described by a Sinai walk of domain walls.

In 2D, dynamics map onto the low-temperature random-field Ising model.

Abstract

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.